Supposedly this is rather new (if a facebook friend is reporting accurately - seldom a given!)

US: (877) 565-8860 Canada: (877) 330-6366

Trans Lifeline is a 501(c)3 non-profit dedicated to the well being of transgender people. We run a hotline staffed by transgender people for transgender people. Trans Lifeline volunteers are ready to respond to whatever support needs members of our community might have
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More details on their website, a crisis hotline "staffed by the true experts on transgender experience, transgender people themselves."

I hate to be cynical, but the linked page you shared for TLL looked amateur and a little strange. I did a google search of Trans Lifeline and wiki which led me to a pseudo wiki on this non-profit which contained some serious allegations.  
I'm sure there is benefit in receiving counseling from a fellow trans person, however one cannot overestimate the value of professional skilled experts staffing the crisis line.

You're right, of course, to recommend some vetting.
(I, as a mildly abashed and oft times punished -for_fun- mere chaser, albeit with much respect and heart, have done no such thing.)

Could be someone calls and it's a well-meaning Mormon on the other end of the phone trying to get transgender people to atone for their sins, but on the face of it, the website looks quite well meaning.

A little more digging via the new link below gives me a somewhat favorable impression.
(And further verifies my skepticism about my Facebook friend's claim that it was new - it's apparently been around since November 2014 ... the Facebook friend is a sweet old lady and a true "Heart Of Gold".)

from a recent article in the Huffington Post (https://www.huffingtonpost.com/entry/americas-first-transgender-suicide-hotline-is-now_us_5a3d253ee4b0df0de8b0648c), which it has since corrected at the bottom of the article).
Anecdotally, I can convey that last year during the holidays I was going through a rough spell and being able to speak to somebody at the TLL on Christmas Day was helpful (granted, I wasn't having a full blown crisis).
I also know of one other tgirl escort that I referred to them and she had a positive experience as well.
For what its worth.
warmest hugs,
Kacy