I like where it’s going. However, I can’t decide which variation works best. L∃DG∃R probably looks best on its own. But TH∃.net is powerful as “The Net” (i.e. The new internet - I even like N∃W.net in that context)… ∃.net is also clean and descriptive of an alternative internet, and probably works most in complimenting the ‘∃’ token. Again, just not sure which works best for me - but I like them all

EDIT: I agree with you re: Lightning looking better without the backwards 'e'. And your reasoning for it overcoming any initial negativity makes good sense... And I'm also not thrilled with Graffiti in any variation - probably because of it's loose association with vandalism and rule-less activity.
EDIT2: I forgot about Rails - I don't mind it at all. But it doesn't surpass other options for me. I like the combination 'Lightning Rails' better than Rails on its own...While you seem not to be leaning toward Matrix anymore (maybe a dApp name), I reckon MATR∃X looks/sounds better than M∃TRIX (IMHO)