VS now has its check-in counters in T2. This is a relatively recent move. I flew out last Friday and stupidly went to TBIT and had to walk back to T2.
As noted above, you can then go through security at T3 and walk through the connector, or walk over to TBIT, whichever you prefer. Depending on the time of day, T3 might be more efficient, especially if you have Clear.
And I can confirm that it's the Star Alliance lounge located above PF Chang's in TBIT, although you should also be able to use the Skyclub in T3. It's about a 15-minute walk from the Skyclub to the TBIT gates, and less than 5 from the Star Alliance lounge.
You'll probably need to show your Skyteam FF card for access, the Skyclub systems aren't as seamless when confronted with Virgin flights. I'm Diamond and have the Amex Reserve card but they wanted to see my Amex even with my Virgin boarding pass (and I bought the Delta codeshare!)