> Practically impossible,
Yes, most likely it won't be done, but that doesn't mean impossible. Just four times farther than the Moon. Flight to the Moon - 4 days, so maybe a couple of weeks here - at most. Getting to Moon orbit from translunar - about 1 km/s, getting back - about the same, here it won't be more.
> especially when building another JWT would cost less,
I highly doubt. JWT is a unique device - telescope at the bleeding edge of capabilities of humanity. And in comparison we had close to 300 manned flights, about 10 of which - above LEO, and more than half a dozen of space tourists - no offense intended, just in case. So, no, I don't believe a manned spacecraft for a longer-duration mission can't be created in a few years.
And the space tech capabilities are actually higher than in 1960-s - look at the SpaceX progress.
> take less time (just do it again, but better!),
Less maybe than those 2,5 decades it took first. But less than 5 years? Unlikely. And in 5 years you may have Starship flying, Starliner flying, Dream Chaser flying, SLS/Orion in a better shape, Falcon-9 Heavy with more flights, possibly Vulcan getting ready - Vulcan has some advanced booster stage, by the way, suitable for more complex missions.
> and most importantly, risk fewer lives (0, by my count).
Possibly - again, in L2 we don't need to land or lift off, while we're still going to to that with the Moon, so I'm not sure if L2 mission would be riskier than a Moon landing flight. But in exchange we'll have those two benefits:
1) service a unique device
2) gain important experience in human spaceflight
Those aren't small benefits.