Ch13:1 (Mr Elton) Ch14:1 (Mr Weston) Ch15:5 (1Mr Elton, 2 Mr John Knightley, 2 Mr Weston) Ch16:0 Ch17:0 Ch18:3 (1 Frank Churchill, 2 Mr Knightley) Ch19:0 Ch20:1 (Jane Fairfax)

Chapter Thirteen:Mr Elton:"'Exactly so, indeed. - She will be missed every moment.'
This was very proper...but it should have lasted longer".
Mr John Knightley doesn't lie, but he does carry on like a pork chop. I suppose it is a sign of their intimacy, that he should be so frank about going out and staying at home, when alone with Emma (he contains himself quite well when Elton joins them). Really! A single Christmas outing, to their closest friends, a visit even Mr Woodhouse can contemplate. A moment's consideration for his young hostess ought still his tongue, if not his indignant heart. He can whinge quite as well as any Woodhouse, and without the excuse of a weak head or constitution. Emma handles him well.

Chapter Fourteen: The subject of the evening is Frank Churchill, specifically Mr Weston is "expecting Frank...I had a letter from him this morning, and he will be with us within a fortnight"
Mrs Weston does not believe the letter. She candidly admits "There is jealousy".
Jealousy is a one-sided emotion, and the possessor of the coveted object is typically not the sufferer. It seems unlikely to me, when Mrs Churchill has enjoyed the satisfaction of keeping the boy from attending his fathers wedding, that she would be still more determined to prevent Frank Churchill visiting his father at the tail end of the festive season. The most bitter of custody-battlers would be disposed to grant a half-hearted and too-late concession like a brief mid-winter visit on short notice, after such a triumph.
I see similarities between Mr Weston and Mr Wickham when speaking of Mrs Churchill: "I never allow myself to speak ill of her...I would not say it to anybody else, she has no more heart than a stone...and the devil of a temper". When he takes advantage of that peculiar intimacy one enjoys as the host of a dinner party addressing the guest of honour immediately after carving, he seems quite unaware that he has gathered half a dozen eavesdroppers to the table - "this is quite between ourselves; I did not mention a syllable of it in the other room". His knowledge of Enscombe cannot equal Mr Wickham's of Pemberley ("I have never been at the place in my life"), but his representation of the personalities is as vivid.
If Mr Weston never talks of the matter, how Isabella can so confidently assert "every body knows Mrs Churchill"? At least her remarks about what a bad mother Mrs Churchill would have made, are uttered while Mr Weston is in another room.
Emma also distrusts the letter, but she suspects Frank Churchill of putting it off. The dilemma of his arrival or non-arrival is a mild sort of cliff-hanger at the end of the chapter.

Chapter Fifteen Mr Elton is delighted to "confess that the nature of her complaint alarmed him considerably" but before he is given any opportunity for further pretense, Mr John Knightley comes in, determined to create "a storm of snow out of the half-inch that had fallen, before the clouds had parted and the wind had dropped and all is hushed tranquility. He is unscrupulous in his attack on Mr Woodhouse "for of course you saw there would be snow very soon" and on his wife. Mr Weston only makes things worse by revealing his lie of omission "lest it should make Mr Woodhouse uncomfortable" and adds to Mr Woodhouse's fictitious comforts with the assurance that "accommodation might be found for everybody."
Mr Elton's profession of love aside, the rest of the chapter is all declared truths and absolute sincerity.

No lies at all in Chapter Sixteen

Chapter Seventeen Mr Elton's letter has exaggeration in every second clause, but it was not written to deceive Mr Woodhouse, more to communicate his resentment to Emma. No lies in her visit to Harriet, either.

Chapter Eighteen We receive confirmation from Frank Churchill that his previous letter was fodder for his fathers false hopes, and his current letter seems to supply more of the same. Now Emma blames the Churchills for his absence, but presently adds "It is very unfair to judge of any body's conduct, without an intimate knowledge of their situation. We ought to be acquainted with Enscome, and with Mrs Churchill's temper, before we pretend to decide upon what her nephew can do." (not consistent, but while she exaggerates and plays devils advocate, she does not say anything she knows to be untrue).
Mr Knightley exposes the fallacy that Mrs Churchill kept Frank from attending his fathers wedding by pointing out "A little while ago, he was at Weymouth. This proves he can leave the Churchills."
There is not a lot of falsehood, and quite a lot of insight to be found in the moralising that follows - but Mr Knightley is prejudiced against Mr Churchill ("nothing really amiable about him") and clearly has thought of Frank Churchill and the pain he has caused Mrs Weston more than once in the past two months, in spite of his assertion that "he is a person I never think of from one month's end to the other."

Chapter Nineteen Emma might feel guilty for failing to call on the Bates, but Miss Bate's supply of comforts does not seem to be scanty - the location of Jane Fairfax's letter underneath Miss Bate's huswife would imply that Emma was rather interrupting their pleasures than augmenting them. We can infer that "The second and third rate of Highbury" include Mrs Cole. We learn again that no letter is private property in Highbury as Mr Elton's letter to Mr Cole is related, and again as Miss Bates takes Emma's implausible "I am extremely happy" to be a "wish to hear what [Jane] says".
Mrs Cole's inquiries after Jane seem to have been based on the same calculations as Emma's, and Emma's good fortune in not falling in with her might be due to Miss Bates wielding the letter, like garlic at a vampire. Emma spots an inconsistency in Jane Fairfax's intentions straight away "But, in spite of all her friend's urgency, and her own wish of seeing Ireland, Miss Fairfax prefers devoting the time to you and Mrs Bates?", and Miss Bates highlights another "A long time, is it not, for a cold to hang upon her?", but none of the polite deceptions,delusions and inconsistencies in this chapter amount to a provable, fully-blown lie (yet).

Chapter Twenty The narrator tells us of Jane's resolution to do her governessing duty, against the inclinations of her friends, which is very commendable, but adds the less commendable revelation that the "account to her Aunt contained nothing but the truth, though there might be some truths not told." This is followed by hints that Jane's health might not be the real reason for staying in England. The narrator vouches nothing with certainty, preferring to quiz us with the motives of the Campbells for acceding to her decision. (My guess for the three motives would be 1/ Colonel Campbell's concern for Jane's health in making the trip 2/ His wife's concern for Jane's ability to bear the parting from all her friends on departing from Ireland and taking up governessing, given her lack of spirits since losing her dearest friend to marriage 3/ His daughters concern on losing her marriage to her dearest friend.)

I think Emma is a little unfair in blaming Jane for her aunt's behavior - if Jane had ate a hearty breakfast and made no presents, her aunt would have as much to say. Jane's thanks and praise on Emma's playing might be mere politeness, but it doesn't follow that her aim was to show off. Jane might take pleasure in playing and Emma in performing, and one not understand the pleasures of the other.
Nor can I wonder at Jane Fairfax's reluctance to give Emma an honest opinion of the suitability of the match between Mr Dixon and Miss Campbell, or her own value for Mr Dixon's company, or an assessment of Mr Dixon's character. I wonder that Emma, who places such a premium on elegance, should ask. The subject of Mr Frank Churchill is a different matter. Emma's association with the Westerns gives her some motive beyond impertinence for asking, and her leading questions are not intrusive or offensive. Here, it would be easier for Miss Fairfax to say 'yes, yes, yes' than to be so suspiciously reserved.