Lindelof is a well-known Star Wars fan from way back in the day, but had been reticent to work on the Disney version of the franchise due to his numerous brushes with fan backlashes. Lindelof rose to fame for his work on Lost (2004-10), which he co-created with J.J. Abrams and co-showran with Carlton Cuse. The show enjoyed critical acclaim and commercial success for most of its six-season run, but had a messy finale which remains somewhat controversial (although time seems to have been kinder to it than Battlestar Galactica's near-contemporary finale).
Lindelof then attracted much more negative press for his work on a batch of films from beloved SF properties: Star Trek (2009), Alien prequel Prometheus (2012) and Star Trek Into Darkness (2013), which were all slated to some degree. Lindelof's name was in danger of becoming mud, but he staged a major career resurrection with the HBO drama The Leftovers (2014-17) and the mini-series Watchmen (2019), which left his skills in demand once again.
The prospect of a Lindelof-written Star Wars movie is interesting as long as he brings the quality and class that he did from The Leftovers and Watchmen, distinctly less so if it's more at the Star Trek Into Darkness end of the quality line.