The space elevator to the lunar surface that 'could be built today'(dailymail.co.uk)
dailymail.co.uk
The space elevator to the lunar surface that 'could be built today'
http://www.dailymail.co.uk/sciencetech/article-2194170/The-space-elevator-lunar-surface-built-today.html
A craft parked at the Lagrange point would be too far from the moon to be practical, and there remains the issue of differential rotation between the parked craft and the moon.
For the earth side, they're planning a balloon at a 2 kilometer height. That is at least feasible. But neither of these proposals represents a way to get cheaply to the moon, their promotional literature notwithstanding, because of the huge gap between the earth's tethered balloon and the other terminal orbiting the moon.
And all of these ideas require materials (for the tethers) that do not exist now or in the foreseeable future.