This is a very interesting fight, in my opinion.
This would not go down like Forrest vs. Anderson, as Rashad is a completely different fighter than Forrest.
First of all, Rashad has the wrestling ability to take Anderson down. Unlike Forrest, Rashad was at one point known to be a wrestler, and he was humbled in his fight against Machida, so he knows that striking isn't the best way to go against guys who are better than he is at striking. As such, he will try and use his wrestling get Anderson down and do what wrestlers do, control and damage from the top.
Standing it would be much harder on Rashad. With that said, though, he isn't slow like Forrest and after fighting Machida, he will have fought someone who has great timing and would at least have some experience fighting guys like that. Of course, if this was a striking battle, Rashad would most likely be finished at some point, but I see him using his speed just long enough to get the takedown.
I'd most likely pick Anderson to win this fight, based on the fact that he is looking unstoppable and if he can avoid the takedown, he will give Rashad a good beating.
As far as if the UFC has the power to make Lyoto fight Anderson, the answer is no. No fighter can be forced to fight the other if they do not want to. All the UFC can do is throw money at them and hope they take it.