What documents are needed for TM30 lodging in Thailand?

If you are saying your landlord has already submitted your info for your arrival into the online TM30 system, then all they have to do is take a screenshot of their submission and you simply print it out and keep it as your proof of filing. This is perfectly acceptable and you don't need to go get a paper version from immigration. Tell your landlord that there is an option on the TM30 portal to check submissions by date, which will search for and display results, and they then screenshot that search result page which shows your details that were submitted into the system. I would say the vast majority of foreigners have screenshots of their online filed TM30s, not some old fashioned paper receipt from immigration. I've attached an example as a comment below, of what the proof will look like, whether filed in person, via the online TM30 website, or via the TM30 app. In your case, if your landlord filed online, they will send you a screenshot that looks like the yellow image in the middle. That's what you print and keep as your proof of filing. Nothing further is needed for you to do.

For the online system? Book and title deed in addition to your list to setup an account. Then for foreigner passport data page, visa, entry stamp and tm6 (if have).

File by mail. All of the above as copies plus application and return postage envelop.

As far as I am aware your landlord does your TM30 not the renter, as they are liable for the fine if its not done