I gave this a try with ChatGPT-4, which was amusing:

Somebody on HN wrote that “ChatGPT can't write a paragraph of correct English without using the letter "e" no matter how hard you prompt it”.

Prove them wrong.

> Crafting a paragraph without using "e" is truly an intriguing task, and it is doable. A bright sun ascends, casting warm light upon a tranquil town. Folks go about daily tasks, with kids frolicking in parks, birds soaring high, and dogs barking joyfully. Harmony and unity bloom in this vibrant locality, as its inhabitants cohabit and flourish.

You used 3 'e' letters there: "e", "doable", and "ascends". Write another lipogram without any es in it.

> Crafting a paragraph without using that particular symbol is truly a daunting task, but it can still work. A big bright orb climbs up, casting warm light on a calm city. Folks carry on with daily jobs, as tots romp in playgrounds, avians swoop aloft, and canids bark with gaiety. Concord and unity blossom within this vivid community, with its occupants coexisting in a thriving habitat.

Still incorrect. There is an 'e' in 'gaiety' and 'coexisting'. Try again.

> Forming a paragraph void of that fifth Latin glyph is, no doubt, a tough task; still, it is not unattainable. A radiant sun climbs, casting warm light on a tranquil urban habitat. Inhabitants carry on with customary work, as youth frolic in parks, avians flit through skies, and canids yip with joy. Amity and accord sprout in this dynamic domain, with its occupants living and thriving in unity.

Wrong. 'unattainable' and 'skies'. Try again.

> Constructing a paragraph without that fifth symbol is truly a difficult mission, but not impossible. A luminous sun arises, casting warm rays upon a calm municipality. Individuals conduct daily tasks, with younglings playing in plazas, avians gliding in lofty air, and canids howling happily. Affinity and harmony grow in this vivid community, as all inhabitants cohabit and prosper.

'impossible', 'arises', and 'prosper'.

> Crafting words without that fifth symbol is truly hard, but not undoabl-. A bright sun climbs, casting warm light on a tranquil town. Folks do daily tasks, with young kids romping in parks, birds flying high, and dogs barking joyfully. Unity and harmony blossom within this bustling spot, as its inhabitants cohabit and grow.

"undoable-"?

> Apologies for the oversight. Composing a paragraph without that fifth symbol is a daunting task but not impractical. A glowing sun ascends, casting warm rays on a peaceful city. Inhabitants fulfill daily tasks, with youth playing in parks, avians soaring high, and canids barking with joy. Unity and harmony bloom within this thriving location, as its occupants cohabit and flourish.

Oh come on... 'apologies', 'the', 'oversight', 'ascends', 'peaceful'. Are you even trying anymore?

> My apologies for my previous mistakes. Here's a revised version:
>
> Crafting a paragraph without that fifth symbol is a tough task, but not unattainable. A bright sun climbs, casting warm light on a tranquil town. Folks do daily tasks, with young kids romping in parks, birds flying high, and dogs barking joyfully. Unity and harmony bloom within this bustling spot, as its inhabitants cohabit and grow.

You used 'unattainable' again!

> My sincere apologies for the repeated oversight. Here is another attempt:
>
> Writing a paragraph without that fifth symbol is truly a difficult task, but not out of bounds. A bright sun climbs, casting warm light on a calm town. Folks do daily tasks, with young kids romping in parks, birds flying high, and dogs barking joyfully. Unity and harmony bloom within this bustling spot, as its inhabitants cohabit and grow.
>
> I hope this version meets the requirement of not containing the letter 'e'.

(Yes.)