Have any Foundry missions you've played really struck you, that they should have a certain soundtrack?
Here are a few examples. I was playing Soriedem's "Claw" series, and when I hit the third mission, right as I entered the Battledome map, this song in my library began...and the timing, the sound of it, AND the lyrics were an absolutely creepy, accurate fit with both the visuals in the mission and and what his character of Spectrum was saying. One effect even captured the fanatical crowd right as I got into the middle of them!
Another example was with Denizen's "Conjoined" mission. This was the music I found myself thinking of (minus, perhaps, the final part of the song) as I entered the latter half of the mission and my captain made a really huge, mind-blowing, and beautiful discovery.
I haven't particularly thought about music as attached to other people's missions. However, I often use song titles (or lyrics) for mission titles and the song usually has at least something to do with the mission, sometimes in a minor way and sometimes in a major way and I'm often listening to that song repeatedly while I make the mission.
For instance (none of these have explicit lyrics btw):
Raktajino in a Jar is based off the story told in the song "Whisky in a Jar," with a Star Trek twist of course. Here's my favorite version, the Metallica cover:
Somewhere in Time comes from lyrics in the Kamelot song "The Haunting" part of what the song is about is a man realizing he's with someone because she reminded him of a past love, which isn't exactly what's in the mission but similar. Plus it fit with the time travel theme.
Sink the Bismarck! comes from the old Johnny Horton song of the same name. I drew a lot of inspiration from the actual events surrounding the Bismarck's campaign in the North Atlantic in World War II (such as the HMS Hood getting sunk in one shot) so the song seemed appropriate, even if the mission isn't an exact historical correlation.
My contest mission Land of Hope and Glory comes from the Turisas song of the same name which is about Vikings returning home, and part of the mission is that you are far outside Federation space and you must return home through many perils.
I often mentally set certain missions (not just Foundry ones, but Cryptic missions and even grinds) to music from certain Trek movies and TV episodes. One that comes to mind is "The Drones Attack" from the Star Trek Insurrection soundtrack. The last half of it in particular is great for large-scale space battles. (In the movie, it's the piece that plays as LaForge ejects the warp core and detonates it.)