As Cliff notes in comments, the objective function for LDA is non-convex, making it a multimodal problem. That is, you can expect any given run to be locally optimal; you cannot expect that any given run would outperform some other run from different starting points.
To choose between multiple runs, consider this from another paper on variational methods by LDA creators David Blei and Michael Jordan (emphasis mine):
Practical applications of variational methods must address initialization of the variational distribution. While the algorithm yields a bound for any starting values of the variational parameters, poor choices of initialization can lead to local maxima that yield poor bounds. We initialize the variational distribution by incrementally updating the parameters according to a random permutation of the data points. (This can be viewed as a variational version of sequential importance sampling). We run the algorithm multiple times and choose the final parameter settings that give the best bound on the marginal likelihood.
They were writing about Dirichlet process mixtures, but the principle of selecting the run that best predicts the data carries. Also consider selecting based on perplexity of a held-out test set.
