We're on track for a manned moon mission in approximately 10 years, and the 'best minds' view building a robotic refueling station in cis-lunar space as the ideal means of making the launch realistically happen, owing to the issues of fuel weights. The rocket to do this mission doesn't exist, the space craft to go there doesn't exist, and the designs we do have (crew dragon, soyuz) aren't easily retrofitted to the mission requirements of going out to L2.
Theoretically solvable, yes. Practically impossible, especially when building another JWT would cost less, take less time (just do it again, but better!), and most importantly, risk fewer lives (0, by my count).
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.
The statements above are wildly optimistic, and don't actually take into account the actual capabilities and capacities of the launch vehicles in question. Furthermore, you're showing an extreme disregard for the actual engineering problems at hand here. It's a multi-decade process to design, build, and certify a launch vehicle _for LEO_. Handwaving "we can do it in 5 years" because the sales teams at SpaceX said so is, frankly, not a real answer. Talking about the "good state" the SLS/Orion are going to be in is, frankly, optimistic to the point of being naive.
Spewing factoids about spacecraft that don't actually exist beyond a "we blew it up on a launch pad" isn't an answer - it's a pipe dream.
Furthermore, you've deftly evaded even acknowledging the core problem - we don't have a space craft with an engine that can do the "back again" part of an L2 mission. That capacity literally doesn't exist right now. You can't just whistle up a rocket that works a few million miles from home.