Edit #2, Feb 10th:

an additional idea is to just name the blockchain Ǝ, ThƎ or LƎDGƎR.

Note it’s not as critically important that users be able to easily type the domain name for the blockchain (as opposed to the domain for the dApps), as they will not be going there directly. Instead they will be accessing dApps or the Google Playstore for the mobile app(s) for the aApps.

After sleeping on it, and bearing in mind the above, I'm now in favour of plain Ǝ over LƎDGƎR. It posesses a simple elegance and suggests a radical methodology at work - agreeing too with what @johnnyflynn wrote:

∃.net is also clean and descriptive of an alternative internet, and probably works most in complimenting the ‘∃’ token.

If you're preferring the Lightning emphasis, a name I'll throw into the pot is now rejected: LIGHTNƎT. Admittedly only one letter away from a Python interface to Darknet I found (replacing this name after reading your latest post) and thought again, choosing LIGHTLƎDGER ; admittedly a portmanteau, which you were trying to avoid, but I think that "light" when combined in the context of the ledger implies Lightning (if that is still desirable?) while being snappier. And it is made unique and iconoclastic by the inclusion of the Ǝ. I chose to only reverse the first "E" in order to make it more easily recogniseable, while at the same time retaining its distinctiveness.

Still not feeling love though for Affinity or GRƎFFITI, even though you gave compelling arguments in their favour.

both Rails and Lightning associate emphatically and directly to transaction latency and scaling.

[Rails] It’s very unique and stands out well compared to extant Top 100 altcoins.

Out of the two, Rails would be my choice.