Under what conditions may a colorblind pilot fly a Light Sport Aircraft legally?
What I assume you are talking about is the drivers license medical loop here in the US that allows you to fly LSA aircraft with only holding a Drivers License (in lieu of a medical certificate). You can find the full regulation here but there are a few things you should know. 

First off you need to see what your local state requires (since drivers licenses are issued by states not a federal body like pilots licenses). If your state has color blind restrictions on drivers licenses you may have an issue 


  (i) Comply with each restriction and limitation imposed by that person's U.S. driver's license and any judicial or administrative order applying to the operation of a motor vehicle;


If you are stepping down from larger planes into LSA planes you can not use the drivers license if you have ever lost a medical cert


  (iii) Not have had his or her most recently issued medical certificate (if the person has held a medical certificate) suspended or revoked or most recent Authorization for a Special Issuance of a Medical Certificate withdrawn; and


The catch all clause that may make the colorblind condition an issue is the last requirement in the FAR 


  (iv) Not know or have reason to know of any medical condition that would make that person unable to operate a light-sport aircraft in a safe manner.


There are lots of light signals used in aviation that a red/green color blind person would have issues with. According to this article color blind LSA pilots are restricted from flying into where color light signals may be used (these signals include but are not limited to tower light signals and ground based warning lights like those in the DC area). If your state issues you a color blind restriction on your drivers license it holds here as well, 


  Of course, any limitations placed on the driver's license would also apply to flying, and a person must always be physically able to perform the flight safely.


Furthermore it seems that according to this article you can have the restrictions lifted if you can pass a color blind test (I assume this applies to both the LSA restrictions as well as the regular PPL restrictions)