Edited to answer questions in the comments.
I live in an oldish house, about 125 years old. I'm a renter so I know a lot less about the house than a buyer would but have a friendly relationship with the landlords, hence room for home improvement.
I have a terribly uneven lawn in my backyard and need to level it for safety reasons as well as aesthetic ones. It's vaguely bowl shaped, with ripples and bumps, especially near the fence line. It's also made up of many different plants, including wild violet.
My neighbor feeds local wildlife and my yard is surrounded by walnut trees, which has turned it into a small wildlife highway. I know from other questions here the rodents can burrow under the lawn, this might be part of why I have so many ripples.
I know that some plants prefer to be planted in the fall and get to overwinter (like tulips) and some plants prefer to be planted more in the season you expect to grow them in (like pansies).
I live in USDA plant hardiness zone 5A and winter is oncoming, which leaves me time to do lots of research for next year. This also means that the ground will freeze and snow will blanket the lawn for many, many, many months. We also typically see a relatively wet summer and my yard currently does not drain super well, which means that puddles form.
I don't want new grass to freeze or flood. When should I level my lawn to best balance these factors?