Load Factor doesn't pay any bills.
But, one thing to remember is that the Profit figure you see on the Route page, is gross profit. It doesn't take into account any costs of operating that route, only operating that flight. So if the profit is really low, it may actually be costing you money even though it appears to be making a profit. There really is no good way to see this.
Ultimately though, as long as you're making some level of gross profit, it's quite likely your best bet to operate the plane on the route regardless. At least unless we're talking about a really low profit figure (like, say, under $2K/day).