DLC for games already started

Hello

I am currently playing Mass Effect 2. I bought the Mass Effect Trilogy box set, so I have all 3, and I'm doing a complete playthrough.

Mass Effect 1 came with all DLC included, and I was surprised to find out that ME2 didn't - I am missing stuff like the Lair of the Shadow Broker. Anyway, my question - I am already in the middle of playing, just finished Horizon. If I buy any DLC, will it be included in this game, or do I need to start a new playthrough?

This is very important for me, since I probably won't have time for another playthrough, and I don't want to throw away money for no good reason.

Thank you!

PLEASE NO SPOILERS!!!!