I have Hitachi TX100 and I started noticing blue haze in different parts of picture. Blue prism has probably some burns (in corners and where subtitles usually are). So i was thinking if i could trick my projector to run without lamp, i could run Jscreenfix for couple of days (weeks?) and get rid of these burns.

There is no blue prism. The prism is after the three panels in the light path and combines the light from the three on its way to the lens. You have a blue LCD panel, polarizing filters, dichroic mirrors, and perhaps UV filters. You cannot reverse burns in these types of projectors. Most will not run without the lamp anyway, but it does not matter. There is no reversing the damage if you have burned polarizers, filters, or panel.