In light of your answer and per my previous post, your objective function doesn't make any sense.
Anyhow, if there are 24 sets of 2 double-sided inequality constraints, avoiding binary variables by "brute force" solving separate optimization problems for each combination of binary variable values won't be viable. So I don't see how you are going to avoid binary variables. So you'll need the version of CVX and solver which can accept binary variables.
You could relax binary variables to
0 <= l1 <= 1
0 <= l2 <= 1
But that won't be equivalent to the original problem. It will provide a lower bound on the optimal objective of the original problem, though. If it turns out that the optimal l1 and l2 of the relaxed problem are 0 or 1 in all components, then the solution to the relaxed problem is feasible and optimal for the original problem.