The consultancy was set up three years ago by Adrian Read with former Polydor Records colleague Chloe Melick.
The agency's clients include Lady Gaga, Alt-J, Chvrches, George Ezra and London Grammar - all of which have been nominated for Breakthrough act at the BRIT Awards. The agency also represents Bat For Lashes, Kelis, Weezer and Wilco.
Lawton joins from Murray Chalmers where he was a key member of the team launching BRIT Critics' Choice 2013 winner Tom Odell and has also worked with Muse, Suede, Patrick Wolf, Radiohead and The Stone Roses. His appointment follows Anna Mears who joins from Dog Day Press. She started her career at Warner Music.
Adrian Read, Inside/Out co-director, said: "We are incredibly proud of what we have achieved during the first three years of Inside/Out and to have played a part in the critical and commercial success of so many brilliant artists is a real honour. By adding publicists of the calibre of Frazer Lawton, following Anna Mears’ arrival last year, we are showing that we are committed to continuing delivering high quality artist publicity for many years to come."