The main advantages I see with lithium is the super fast re-charging (I think a deep cell take 6 to 8 hours to charge back up) plus they run constant voltage as they drain which keeps the fridge running.
I run the the Odyssey for my main and SLEE has a tray to fit a group size 31. For my aux battery I run a Lithium Valence. Some people get the battle born for $1000+ or you can look around and get a Valence for way less and it's just as good.
One rule about Lithium you do need to isolate it from...