Wind gusts of up to 40 mph made play difficult at the Golfclub Munchen-Nord.
'It was always coming from the side of the fairways, which made the choice of club very difficult,' Lima said. 'Any score out there under par was good.'
The Portuguese player has won once on the European Tour -- at the St. Omer Open in 2004.
Sweden's Fasth, who held the overnight lead, shot a 73, with a birdie on the 18th.
Peter Hanson (74) was second at the start of the day, but had four bogeys in his first five holes
Paul Casey (74) also slipped off the leaderboard, and Paul Broadhurst, who was 5-under after 36 holes, shot a 79.
Bernhard Langer (68) -- who turns 50 in August -- and Scotland's Alastair Forsyth (67) gained the most from having a morning start before the strong winds. Langer's score could have been better had the German not found water twice late in his round.