much depends upon context.
another option: "...If I should find the lost treasure, I shall / I will (I'll) keep it..."
Should here is expressing a condition, that if this happens "someone finds a treasure," then the finder gets to keep it.
You are correct. It seems unlikely than you can use "I'll (or the auxiliary verb will) twice in a sentence containing the conditional "if" clause. You are expecting something to occur (some condition come true) now in the present tense and indicating what you will do with afterwards as a direct consequence or in the future.
If I find the treasure today, I will exchange it for cash tomorrow at the ....
If I find the lost treasure, I will become the richest person....
Hope this helps.