I Have Lichen Planus on my Gums. Would Brite Smile Be Safe?

Your condition with lichen planus might be exacerbated by using whitening agents.  I would recommend doing professional trays and start slow (maybe 15 minutes) at first to see how you respond.  

I have treated many patients over the years to whiten that have Lichen Planus. I would wait until symptoms, if any, are minimal. Custom tray whitening is good as mentioned above. However, I would also consider in office whitening like Zoom. The teeth are exposed and the gums and all other mouth tissues are protected with a barrier. This way the bleach  would be prevented from irritating the mouth.

Since you will be introducing chemicals to the oral mucosa, there may be some irritation. Starting slow with take home trays and increasing exposure should give you an idea of your threshold. A well fitting tray system (not the flexible type found in most dental offices) should contain the gel and therefore limiting leakage and exposure to the gel.