I've not had green lemons ripen successfully. If they are full-sized tho and just beginning to turn yellow you may have success.

I generally pull them when they are yellow and leave them in a bowl to ripen further.
You might want to try making marmelade.
Carol

Citrus after being picked will only rot. They will not get sweeter or more "ripe". Al

In my experience, they do not rot after picking. They only shrivel and change color from green to yellow or orange. If very immature, then they change to brown after shriveling. They would then dry up like hardened corks (was talking of calamondins here). Immature ones never ripen even if they change color. The almost mature ones will ripen slightly. The fully ripe ones when picked would have slight sweetening due to the drying process and limited amount of enzymatic reactions in a warmer and drier indoors environment. Citruses are not fully climacteric, perhaps only to a very slight extent. Citruses are best ripened on the tree.

Calamondins, lemons, limes these will ripen slightly and even sweeten to a certain extent if you pick them as soon as they are showing hints of yellow on the tree. But never oranges and navels. Even if they are bright orange, they are still sour. The deep color orange is characteristics of California climate, but the oranges are not yet ripe and will not ripen off the tree and still remain juicy.

In contrast, avocadoes are climacteric, and bananas are fully climacteric that even the immature fruits will ripen off the plant.

Why do you have to remove the lemons?

If you don't, others will! :)

Also, sometimes I remove a lot of them at once, it is easier to give them away to lazy friends who wants them gift-wrapped (package in plastic bags). Can't bear to see them falling off and rotting away at the base of the tree.

But I do leave some of them on the tree as long as possible.
Year round, I have them, and sometimes become very "stingy" when the grocery stores hit $1.50 per lemon. While I have them year round, they really peak producing come november to february. It just rains lemons.

Very little in my experience.

I find the less green at the bottom end the riper they are. But the ones with tinges of green provide nice enough tang for fresh lemonade and for cooking purposes like popping in with fresh veggies while they steam to keep them vibrant.

Here's my solution to too many lemons on the tree. I pick the ones that are nearly (small green at the base)or ripe. Then using a potato peeler I peel the best part of the rind. Then I squeeze them (12 on average=1 ice tray) and freeze them in ice cube trays. Then put in a plastic bag and keep in freezer. Same for the lemon peel. Great for fresh lemonade, etc.
You could also call the nearest food pantry/kitchen, church, etc, and donate them. The cost (?) why picking your abundant crop. Everybody wins in this situation.

my lemons have been on tree for months are pretty good size,how long does it take lemons to turn yellow for picking?