I use grid search with bounds for example lb=[ 1 1 1 1 1 1]'/1000; ub=[10 10 10 10 10 20]' but it is computationally difficult so it checks 2 points only. Thus i obtain boundary solution consisting from elements of lb and ub. Correct to test hypothesis x2=0 with LR stat?
Assuming you are asking how good are you approximating the true maximum using this grid search, then there is no absolute answer. It depends on the gradients of the likelihood function relative to the resolution of your grid. You might also have a-priori reason to believe the solution will be on the boundary of the search space-- in which case searching on the boundaries alone makes sense. Except for this scenario, I tend to say your solution can and should be improved.
Assuming the computational difficulty arises from the six-dimensional parameter, you should try gradient based methods (all numerical solvers have some implementation). If the target function is nice and smooth but with many local optima, consider multiple initialization points or maybe a minorant maximization algorithm (such as the EM). If the target function is not smooth and friendly, then there is probably no way of escaping long computations unless you can restrict the solution set somehow.
Bottom line- except for very specific cases, looking on the boundary alone is not a good solution to maximize the likelihood nor computing the generalized likelihood ratio statistic. (unless you do it for the alternative alone, then the ratio can be seen as a conservative version of the GLR statistic and all inference will indeed be conservative).