I'm confused what do you mean by the equations been stable.
The way I would do it is to divide the space into a grid (64 by 64 should be enough), this would make calculations easier, specially using matlab. one of the grid point will be your robot, and another two your two lights. Maybe later on you would like to add a parameter to your robot theta that will determine witch direction the robot is using.
Remember intensity is measured W/m^2 or Power over area, that means that the Intensity is inversely proportional to the square of the distance.
I would match the time step to the time needed for the robot to travel one grid division in the slowest velocity. (remember going on diagonal takes longer, but if the grid space is small enough this might be ignored).
Start with known scenarios and make sure they work fine, like the lights fixed, or traveling on a straight line.
This should be a good first approach, better solutions could be found.
Just out of curiosity, what kind of robot are you using? I used parallax basic stamp some time ago, and parallax have a new microprocessor called propeller whit intrinsic multi threating, worth giving it a look.
I hope this helps you. Let me know if I miss understood your project, and let me know how everything goes.
Best Regards