While I believe it to be very unlikely that there would be a 14th LBT movie there is no harm in hoping and not in promoting even the tiniest of chances with such a petition. Is it likely to achieve the making of another movie? No. Is it likely to cause any harm whatsoever in the proces? Certainly not.
If there is such a petition brought up I am quite willing to sign it. Not hoping for much, but not seeing anything negative about signing it either.
They don't want to make a 14th movie because they knew Movie 13 was gonna destroy the series for good.
With all the frustration you may have about the 13th movie (which I agree was very bad), I do not see the reason behind any assumption of intentional messing it up. I think I read somewhere (and don't quote me on it because I don't know how reliable the source was) that LBT 13 was the first of the movies to be in the red financially. The assumption of people intentionally making a movie bad to loose some money for the heck of it (or which other motives would there be for such a move?) is ridiculous.
What I think is a main problem about the making of further LBT movies is the lack of plot ideas that are not mere repetitions of what has been there before. Many people are ready to blame universals for bad movies or the TV series, but hardly anyone would be willing to come up with a plot that one could turn into a movie not in conflict with LBT as we know it from the earlier movies. It is one of the things that I am acknowledging the TV series for, that they came up with quite a number of plots that, although they were not sufficiently long to suffice for a full length movie, were for the most part not in conflict with LBT from the sequels.