In a specific part of the state or is this just a general question? It's a big state.
Some of the better LMB lakes would include Fork, Allen Henry, Amistad, and others could be included in the list. You can fly fish any of them that time of year, but they are located hundreds of miles apart from each other.
I'd suggest asking about the best lake in the part of the state you plan to visit.
I understand; I can go anywhere and I have 2 weeks. So I'm looking for help narrowing things down. I have timeshare availability at Flint, Wills, and near Lake Fork. But I don' t have to stay at those areas if you have an outstanding choice.
Lake Fork is the most famous LMB lake in the state. So, it should be on your short list of options.
But, I recommend posting this question on the Bass Fishing section of this board. It gets a lot more traffic than the Fly Fishing section and I think you'll get more information on different lakes.
One thing to consider is that many of these lakes will require access to a boat and not all of them have rental boats available. So, if that is a concern, I'd be sure to ask that question while you look.
My pick without a doubt would have to be Athens in April. Fish poppers, gurglers, frogs along pads and over grassy points in the AM, strip streamers over grassy structure during the day. Lots of fish and good shots at bigger ones too.