Somdev, who led two sets to one when rain interrupted the match, returned to clinch it over five sets, 4-6, 6-1, 6-2, 4-6, 6-4, in three hours 11 minutes Wednesday.
The Indian next plays World No.20 Italian Andrea Seppi, who overcame Belgian veteran Xavier Malisse in four hard-fought sets, 6-3, 3-6, 7-5, 7-5.
Somdev, 28, playing the 24-year-old Lukas for the first time, was generally in control of the match, with his better court craft and net play.
The Indian, who returned to the circuit after a shoulder injury kept him out for more than a year, is ranked 114 as against the Slovak's 84.
But Somdev had a better season with a 21-8 win-loss record whereas Lukas struggled to 12-18.
Somdev was steadier of the two Wednesday as he served well, landing a greater percentage of his first serve, and importantly he was in command of the net, winning 27 points in his 29 forays.
When it came to hitting winners, Lukas was far ahead with 49 to Somdev's 30, but in going for ambitious shots the Slovak had committed double the number of unforced errors (73) than his opponent who logged in 36.
After losing the first set, Somdev kept the Slovak in check to take the next two sets before rain sent the players scurrying into the locker room.
When play resumed, Lukas took the tight fourth set, but the Indian got the better of him in the decider.