I cannot really speak for Truly Med, but looking at the pictures, I am pretty sure you can find equal or better places here. Los Angeles always has better food than San Francisco and New York, heh . . . (Yes, I did that on purpose.) I am going to speak more towards mediterranean food and falafels than schwarma. You should try the following places: Zov's in OC, Farmer's Market on 3rd and Fairfax, PitaPit, Papa Hassan's in Orange and there is another place by Orange Circle (right off it actually), Papa Cristo's, etceteras It's probably more of a question of thinking of places, but you should start with those. Post what you think of those and like David Kahn pontificates tell us what you find also . . .
Apologies in advance for the dime store food philosophy that follows.
I'm sorry to tell you this (really), but I've been reading and participating on this board a long time, and the answer to the question "I just moved here from X, and I really miss Y; is there anyplace just like Y here in LA?" is pretty much always "No". (For some reason, it seems to me that most of the folks who pose this sort of question have moved here from New York or San Francisco, maybe because those cities have such amazingly deep food cultures.)
That said, Los Angeles is, at this particular moment in time, one of the most vibrant, interesting, varied food cities in the world. In my opinion, if you spend your time trying to find replacements for the good places you loved in the place you came from, you are destined to be sad and disappointed. If instead, you resign yourself to finding new, different places to love, Los Angeles will take care of you. In an odd way, the best substitute for Truly Med (which, btw, I've been to and agree that it totally kicks ass), is probably Dumpling 10053 or Tere's Tacos or Sushi Gen or some place you'll discover that none of us has yet heard of.
422 E 2nd St, Los Angeles, CA 90012
Tere's Mexican Grill
5870 Melrose Ave Ste 1, Los Angeles, CA 90038
10053 Valley Blvd Ste 2, El Monte, CA 91731