Since for the spheroids to form you need them to accumulate inside the drop, and not on the lid itself, there is actually no difference whether the lid is treated or not. Actually I cannot remember whether there are Petri dishes with treated lids at all. Procedure is as follows - you take the lid off the dish, you pipette desirable amount of drops of your cell suspension in culture media on the lid. Then you pour some media inside the bottom of the Petri dish to conserve the moisture inside. Then you carefully turn the lid over and put it back on the bottom part of the dish. I can't remember now, what volume of the drops we used, but I think it was 50 mkl.
I agree with Mikhail Alexandrovich Borisov . I have never heard of treated lids.
In a spheroid which is a 3D aggregate of cells, the intercellular interactions are favored over the attachment to a substrate. Such conditions will be met only when cells do not create contacts with a fixed support such as the plastic or glass surface of a culture plate, and then they start to self-assemble in loose aggregates. It is the same process that you may observe in embryogenesis or organogenesis.
Integrins and E-cadherins play a key role in this process. The integrins are transmembrane proteins which can bind to extracellular matrix (ECM), if the cells used are able to generate ECM components, and initiate the agglomeration of cells as a network. Then, the homologous E-cadherin interactions tightly pack the cells together and make the structure to evolve into a compact spheroid.