if the information was that they decided to burn tokens, that would help to increase the price, just locking in could not raise the price without new developments on the project, since these tokens are still in the total number of tokens
A token that is locked up can be unlocked at any time. The best precision and trustworthy step would have actually been the burning.
Well, this might make the price to increase, but I do not see much increase, expect there is a major update.
So, burning should be accompanied by a good and strong news.