I had an '07 with many more miles than yours. The only big problem I had with it was a snapped axle. The driver side axle has a rubber vibration dampening ring on it, and salt got up under it and rusted the metal. Minnesota winters are hell on cars. The part was $250 (new from Honda), and the labor was free because I did it myself. Would have been around $800 at a shop. I sold it to my next door neighbor when I got a different car, and he’s still driving it daily with no problems. I’m a bit wistful that it’s gone - that was one fantastic car.
Yours has a potential problem brewing that mine did not. In '07 they used the RL transmission in the TL to get rid of a transmission failure problem that was in the original transmission. The cause was that the 3rd and/or 4th gear pressure switches would slowly go bad, and eventually would cause enough of a reduction in line pressure that the (usually 3rd gear) clutch would slip and burn out. Most people with your vintage of 3rd gen TL have good luck replacing the transmission pressure switches as preventative maintenance. It’s not a very expensive job even at a shop, and I would recommend that you do this whether you go on a road trip or not. Have them exchange the transmission fluid while it’s in there, unless you’ve done it recently. It should be done every 30k miles.
Beyond that, what I would do in your case just for peace of mind is take it to a good local mechanic and ask them to perform the equivalent of a pre-purchase inspection on it. That should catch any issues that might cause problems on a road trip.