Note that the fourth triangular number is $10 = 1 + 2 + 3 + 4$. To make $11$, you want to increase one of those numbers by $1$. However, if you increase any of the smaller 3 numbers by $1$, you will make a duplicate, but we're told that all four numbers are different. Therefore, we must increase the largest number by $1$ to get $1+2+3+5 = 11$. Therefore, $\boxed{l = 5}$. I could do a proof that this is the only possible way to make 11, but middle school isn't really the place for proofs.

Note that the fourth triangular number is $10 = 1 + 2 + 3 + 4$. To make $11$, you want to increase one of those numbers by $1$. However, if you increase any of the smaller 3 numbers by $1$, you will make a duplicate, but we're told that all four numbers are different. Therefore, we must increase the largest number by $1$ to get $1+2+3+5 = 11$. Therefore, $\boxed{l = 5}$. I could do a proof that this is the only possible way to make 11, but middle school isn't really the place for proofs.