It really depends on whether they're looking at LC from a load balancing perspective, a redundancy perspective, or both. If they want to maintain outbound access if a router fails, obviously they need more than one router.
I wouldn't terminate the Links on the LC, but that's just me. In the current environment, I'd make sure the LC has an ip address on each internet link, and also give it a private address. I would see the flow being something like this:
1. User tries to go to the public internet.
2. The request routes through the firewall, and then gets sent from the firewall to the LinkController which then chooses an Internet Link to send the traffic out.
I'd assume the Firewall has an address on the client network and the public network or another dmz of some sort. The firewall's next hop in my example would be the LinkController.