The 19-year-old broke the deadlock at the Stadio Olimpico to put Gian Gasperini's team ahead, two minutes into the encounter.
Barrow converted off Marten de Ron's assist to register his third effort in his 10th league appearance this campaign.
Felipe Caicedo drew Lazio levelled in the 24th minute as both teams settled for a share of the spoils.
The Gambian attacker was replaced by Josip Ilicic in the 52nd minute.
Atalanta, placed seventh in the Serie A table, have now garnered 59 points from 36 games - a point adrift of the Europa League qualification zone.
La Dea host sixth-placed AC Milan in their next league game on May 13.