For the seasonal section, can we also use non seasonal runs. Or if the lobby doesn't change for the season, do we have to submit a run from the seasonal time?

No, you can't submit non seasonal runs on the seasonal category. Although, you can submit seasonal runs on non seasonal categories, if the seasonal lobby isn't faster or presents an advantage towards the non seasonal lobbies.

What if the lobby doesn't have a seasonal version? Then does it not matter what time of year it is?

Once the seasonal lobby is gone, so is the category. The next time it will open again is when the next seasonal lobby comes out.

Nvm, just got an answer since my runs got rejected from the lobbies that dont have a seasonal variant.