Disadvantages
The risk of proton exposure from the solar wind as well as the health threat from cosmic rays is significant. In the Earth-Moon system, the orbit of colonies at L1 - L5 will take them outside of the protection of the Earth's magnetosphere for approximately two-thirds of the time (as occurs with the Moon). Colonies at L1 (located between the Earth and Moon) will experience this to a lesser degree while L2 (located beyond the Moon) will experience this to a greater degree and all of them will be exposed to the little understood plasma sheet of the magnetotail.
In the Sun-Earth system, L1 and L3 - L5 are all outside of the protection of the Earth's magnetosphere. L2 periodically transfers from within the magnetotail, plasma sheet, and solar wind depending on the intensity and direction of the solar wind.
Read more about this topic: Lagrange Point Colonization