Preposition of agent

It depends. I can see three somewhat different meanings here, and they all lead to different choices.

If you want to say "he is carried in a litter", then the litter just describes location and is not really an agent. In this case you would use in with ablative and get in lectica portatur.

If you want to say "he is carried by a litter", then the litter can be considered an agent. Some agents in Latin get a preposition (it's always a(b(s))), but not all do. A rule of thumb is that human agents get the prepositions and thing agents don't. It's a matter of will; if the agent willfully causes the event, it gets a preposition, but if it is a mere instrument, it does not. Thus the agent without preposition is really the same thing as an instrumental ablative. (The instrumental ablative can also be used with the preposition cum.) In this case you would get lectica portatur or cum lectica portatur.

If the litter is an autonomous being that decides to carry you — I am still waiting for the release of the self-driving litter — then a "human agent" with a preposition is a valid choice. In this case you have a lectica portatur.