Lazarus generates 3 file types for projects - *.lpr, *.lpi and *.lps. The first 2 files are necessary.
Should I keep *.lps files in version control system or should I include *.lps files in global ignore list?
IMO, no if you are not sharing the projects. Due to the FAQ, the lps files are "Lazarus Program Session - Personal data like cursor positions, source editor files, personal build modes. stored in XML".