Unfortunately the likelihood ratio test cannot be used this way. It is only for comparing nested models (i.e., one model has to be a logical subset of the other--for example, with some parameter constrained to a particular value in the subset model but that same parameter free to take on any value in the larger model). The Weibull and lognormal distributions do not have this subset relationship, so they can't be compared with an lrt. For non-nested models, you probably have to make comparisons using AIC or some such model goodness measure.
I don't really understand what you are saying about rejecting the null. It seems to me that if you generate the data from a Weibull then you wouldn't expect to reject the Weibull in favor of some other distribution like the lognormal. (Well, maybe if the other distribution were much more flexible than the Weibull, but that doesn't apply to the lognormal AFAIK).
By the way, these statements are redundant:
wblPD = fitdist(x, 'weibull');
lnPD = fitdist(x, 'lognormal');
wblPms = mle(x, 'distribution', 'weibull');
lnPms = mle(x, 'distribution', 'lognormal');
The outputs of fitdist are structures containing the very same parameter estimates that you get from mle.
I hope some of this helps you to move forward.