The first three rounds of the tournament are played over three courses, including the Old Course at St. Andrews, which will be the site of Sunday's final 18 holes.
Lafeber played Carnoustie Thursday and opened with a bogey at No. 10. But he had four consecutive birdies beginning at the 12th hole and, after a par at No. 16, had birdies at 17 and 18.
His round also included a double bogey 6 at the seventh hole, but he got both strokes back with birdies at 7 and 8.
Bjorn, on St. Andrews, closed with four birdies in six holes to grab his share of the lead. Laird played Kingsbarns to a bogey-free 66 while Gonzalez, playing St. Andrews, posted six birdies and 12 pars.
Six other players finished the first round in 5-under 67 while 14 more are at 4-under 68.