According to Isaac Arthur and the like, this is accomplishable with today's technology (given global cooperation, significant fraction of GDP). There are only a few stable points you can go to in cislunar space, the main ones being the Earth-Moon L1 and L2 points.

To resolve YES, construction must have started by Jan 1, 2100 UTC. It does not need to be a single tether to the counterweight station, in fact multiple tethers might even provide for better usability and stability.