I would build it to work with the lid on, just in case it warps later on and the gap grows. My homemade rack has no lids, and I have to use a slip of cardboard to "jam the door" on some of the tubs because the gaps are too big.
I made it work to my advantage by labeling the cardboard slips, allowing me to just move the slips as I move snakes
You can see what I mean in this picture. The 41qt tubs fit my 4-5 foot Honduran milks just fine, the 3-4 footers would be fine in a 32qt though.
Edit: Yes I have dusted it since this picture![]()