Welcome to our forum.
Sounds like you are in a developing V (two persons are the ends of the V and just associate with each other platonically, whereas you are the "hinge" of the V and have a romantic relationship with both of the guys). It's a good thing if the ends of the V are friends, but that's not required. I would suggest letting L and M decide if, when, and how often they will hang out together. Especially in the beginning, they need time to sort through their nerves and misgivings.
You should always try to improve your communication with T and M. Communication is a really important part of making poly work.
A couple of boards I'd suggest you check out on this site are:
Golden Nuggets board
... for the most basic/important info about making poly work
Life stories and blogs board
... for portraits of other people's experiences and what has/hasn't worked for them
Poly Relationships Corner
... for posting your own thoughts, questions, and concerns
I think if you take things slow with T, and communicate often with M about your feelings, you will come out alright. But check out the above links for further guidance.
Glad to have you aboard,