Such a telescope located at the Lagrange point between Earth and moon would be very cool :-)
I’d love that, too!
Depending on the cost of “spaceplate,” there’s no limit on how big telescopes could become. Do you want to see all the smiling faces on some planet in Andromeda? Could become a reality... I guess?
Oops, methinks you are off on your celestial mechanics (smile)! There are 5 Lagrange points in the Earth-Sol configuration and none lie between the Earth and Luna.
L1 is 400k kilometers / 932k miles / 5 light seconds directly sunward from Earth while L2 is its mirror opposite anti-sunward and the destination of the JWST (James Webb Space Telescope). L3 is at the contra-Earth point behind Sol at just a bit outside Earth's orbit. L4 & L5 are at the 'Trojan Points' leading and following Earth in the Earth-Sol equation.
FYI: Only L4 & L5 are naturally positionally stable and, as such, already have detected objects in that area. L1-L3 require station keeping intervention to avoid a 'falling off' problem. As such, there is no current natural occupant(s) already there.