To clarify: "The Rape of the Lock" is extremely witty, but he does it by breaking the very rules he establishes in "An Essay on Criticism."
In "An Essay on Criticism," Pope's notion of "Wit" is difficult to pin down in a few words, not unlike attempting to explain the Japanese notion of "zen." We generally understand "wit" to refer to the quality of being clever, or funny. Pope no doubt includes this definition (as he liberally applies it himself), but his definition of the word is considerably broader. Let's begin with his most quoted lines on wit:
True Wit is Nature to Advantage drest,
What oft was Thought, but ne'er so well Exprest,
Something, whose Truth convinc'd at Sight we find,
That gives us back the Image of our Mind:
As Shades more sweetly recommend the Light,
So modest Plainness sets off sprightly Wit:
For Works may have more Wit than does 'em good,
As Bodies perish through Excess of Blood.
In short, "wit" begins with observing truth in Nature (human affairs, generally), particularly that which everyone observes themselves, but have never expressed as well as the "true" wit. Comedians work on this principle, incidentally: their craft is to think about the little things we all notice but never bother to think about or express (think about it!). When we are confronted with a well-expressed observation we've had ourselves, we are delighted (and often amused).
Further, Pope says that wit is best "set off" by plainness, as opposed to "conceit," which he waxes eloquent about earlier in this same stanza. He opines that "Some to Conceit alone their Taste confine, / And glitt'ring Thoughts struck out at ev'ry Line," and
Poets like Painters, thus, unskill'd to trace
The naked Nature and the living Grace,
With Gold and Jewels cover ev'ry Part,
And hide with Ornaments their Want of Art.
"Conceit," incidentally, is an extended metaphor, often used--primarily by poets--to illuminate an idea. Unfortunately, as Pope points out, it can be like paint in the hands of the unskilled, the metaphor stretched too far, more of a distraction to the reader than a help.
He cautions that a little wit goes a long way, and should be couched in "plainness"--not in splashy "Art." Wit, then, is the measured sharing of well-phrased observations about Nature, the soul of genius.
Determining whether he followed his own advice in "The Rape of the Lock" is a complicated matter, as it is written in the same "clear"--at the time--poetic style as "An Essay on Criticism," which to modern ears is itself unnatural and, well, splashy and showy. To determine for yourself if he follows his own advice, it is first necessary to understand his purpose in writing "The Rape of the Lock."
This mock-heroic poem was written to satirize both heroic epic and what was, in reality, a petty spat a friend of his had had. Thus, in this poem, he goes out of his way to break the rules he said not to break in "An Essay on Criticism."
For example, in his second stanza, he writes: "Sol thro' white Curtains shot a tim'rous Ray, / And op'd those Eyes that must eclipse the Day." He himself is not using "modest plainness," preferring "sol" over "the sun," and there's nothing witty about the cliche of the woman's eyes "eclips[ing] the day."
Soon we read that "Belinda still her downy Pillow prest, / Her Guardian Sylph prolong'd the balmy Rest." "Her Guardian Sylph" (Phoebus, Ixion...)? In "An Essay on Criticism," he recommends studying Homer, a true master, but here, he is like the apothecary he has condemned, who learn over time what doctors prescribe and thus eventually think themselves themselves learned enough to cut out the middleman and write prescriptions themselves: he isn't mimicking Homer so much as (intentionally) using the gaudy language and obscure mythological references of his contemporaries.
Further, he uses very conceits he earlier condemned. Observe:
And now, unveil'd, the Toilet stands display'd,
Each Silver Vase in mystic Order laid.
First, rob'd in White, the Nymph intent adores
With Head uncover'd, the cosmetic Pow'rs.
A heav'nly Image in the Glass appears,
To that she bends, to that her Eyes she rears;
Th' inferior Priestess, at her Altar's side,
Trembling, begins the sacred Rites of Pride.
Unnumber'd Treasures ope at once, and here
The various Off'rings of the World appear;
From each she nicely culls with curious Toil,
And decks the Goddess with the glitt'ring Spoil.
This Casket India's glowing Gems unlocks,
And all Arabia breathes from yonder Box.
He means to say that Belinda, with the help of her maid, dresses and puts on her makeup, but he has spilled a lot more ink than is necessary to say it. :)
The entire "Rape of the Lock" is written tongue in cheek, so no...Pope does not follow his own advice in this (fantastic) poem--by design.