Your laptop has DisplayPort, it is very similar to HDMI, not as common on HDTV's, but does cool stuff like daisy chains.
If the the DP on your T520 is similar to the one on my X220 (it should be, the logo on top of the port should have two "+" next to the D), and it passes the DVI/HDMI signal as well, which means it can use a (cheaper) passive adapter like this
guy. Sadly Monoprice doesn't have any DP to HDMI cables TT_TT, so if you want a full cable instead of just the adapter, Google is your friend.
EDIT: btw, DP passes audio through so you don't need an additional cable for audio.