You are (to my understanding) not required to use Lootlocker in the Jam. You can use your own solution or just an offline score.
I have not yet looked much into the feature list of Lootlocker, however I'd assume it can support more complex scores. If not through the Leaderboard system, then with one of their other features.
But you can always use your own backend. Would be great to see different solutions and compare them. Don't forget to mention any work done before the jam, as is't still a GameJam.