Hi-
I'm a United 777 captain, so hopefully this will help.
Many of our 777s have the new lie-flat seats in business, but there are still a number of them that don't. Aircraft get switched frequently, so it's hard to know well in advance which interior you're going to get. If you really need to guarantee a lie-flat seat, and cost is not an object, the only way to do that would be to go in first class. On most of my flights first class winds up being full. I don't know how many are upgrades at the gate, but it's been rare to see us go out with empty seats in that cabin.
I hope that helps a little.