It is actually very difficult for athletes to play different sports. In the history of the NFL there have been very few real crossover players but the ones that did make it were usually basketball players in college.
Julius Peppers, Tony Gonzalez, Antonio Gates, and a few others were very good college basketball players who also played football, but I can't think of a single guy who played one sport (other than football) in college or as a pro and then made a switch to the NFL successfully.
It isn't just a matter of being big, fast, etc. it takes years of training to play football at the NFL level. Brock Lesnar is obviously a great athlete but he could make it onto a roster let alone the playing field.
People throw out names like Usain Bolt but that guy isn't about to sacrifice his body on a football field when he can be completely dominant on the track instead.
The same goes for LeBron James. He might like to try playing football as an experience but after a few plays he would go back to basketball and never look back.
It takes a different kind of mindset to play football than to play any other sport. For one, it is the ultimate TEAM sport and guys who are used to being individual stars don't fare as well in it. That requires the ability to sacrifice personal stats/goals for TEAM goals and wins. Guys LIke Bolt would not be likely to do that, neither would LeBron for that matter.
Most of this is the same type of stuff we see after the Combine. Everyone gets all moist over some guy who didn't do squat on the field but ran a 4.1 on the track or did 50 reps on the bench and now he's all world... until he actually gets to Training Camp and they find out that the guy just can't play, regardless of all his athletic ability.
Anyone remember the great Macey Brooks? He was a WR we drafted back in 1997 and people were going nuts over him. He was 6'5" 215 lbs and could run like the wind. The problem was that he couldn't run routes and couldn't catch the ball. He bounced around the league for a couple of years because every team thought they could capitalize on his unique athletic skills but he never caught on. He did see the field for a few games with the Bears in 1999 & 2000 but was nothing like what everyone was expecting.
LeBron James would likely be the same. It isn't as easy as it looks to run routes and catch the ball in a real game with a helmet and should pads on with DBs knocking you all over the place and your ears still ringing from the hit you took by a LB or safety who was just trying to knock you off your route (as an OLB I used to love doing that!).
Your peripheral vision is restricted by the helmet, your arms are limited by the shoulder pads, the surface may be hard or slick or muddy and there are guys flying all over the place. You are trying to remember what route you are supposed to run, how to read the DBs to know if you are to break inside or outside or to cut it off short to the "hot route" if they show blitz, etc...
Basketball is a much easier sport to play than football, in fact EVERY other sport is easier to play than football IMO.