Edward Lear was of course a wonderful composer of nonsense verse but let's face it, his limericks are lacking a certain something. To put it in limerick form…

There once was a poet named Lear
Whose limericks were really quite queer
For try as he would
His last lines were no good
That imperfect poet named Lear.
(So insert something better just <here>.)

With that in mind, here are some Learian Limericks that I have improved.
If you fancy a go you can find a selection in need of improvement here on Project Gutenberg.
https://www.gutenberg.org/file.../13650-h/13650-h.htm

There was an Old Man with a beard,
Who said, 'It is just as I feared!
Two Owls and a Hen,
Four Larks and a Wren,
Have all built their nests in my beard!'
(Were found there when my beard was sheared.)

There was an Old Man in a tree,
Who was horribly bored by a Bee;
When they said, 'Does it buzz?'
He replied, 'Yes, it does!'
'It's a regular brute of a Bee!’
(Though I fear it’s a little off-key)

There was an Old Man on a hill,
Who seldom, if ever, stood still;
He ran up and down,
In his Grandmother's gown,
Which adorned that Old Man on a hill.
(Crying, “Once I was Jack, now I’m Jill”.)

There was an Old Man with a nose,
Who said, "If you choose to suppose
That my nose is too long,
You are certainly wrong!"
That remarkable Man with a nose.
(I can pick it with fingers OR toes!)

There was an Old Man of the East,
Who gave all his children a feast;
But they all ate so much,
And their conduct was such,
That it killed that Old Man of the East.
(That from both ends their wind was released.)

I'd say you've improved all but the old man with a beard. I like it as Lear wrote it.

Very good job on the Old Man on a hill!

Agreed, so here is a slightly better old man with a beard

There was an Old Man with a beard,
Who said, 'It is just as I feared!
Two Owls and a Hen,
Four Larks and a Wren,
Have all built their nests in my beard!'
(All appeared when my beard had been sheared.)