The L1, L2 and L3 points are all unstable, but there are nearby orbits that are neutrally stable, e.g. the halo orbits and the orbits described in the article.

The L1, L2 and L3 points are all unstable, but there are nearby orbits that are neutrally stable, e.g. the halo orbits and the orbits described in the article. A spacecraft on one of those orbits will still need to use some propellant to get it back on track from time to time (for "station keeping"), but it's typically not very much propellant. Such orbits have already been used for other missions, such as the Solar and Heliospheric Observatory (SOHO).