Lohse, scuffled in his third Cactus League start, allowing five runs and seven hits in 3 2-3 innings. He walked two and struck out two. Lohse's troubles came in the fourth, when he walked Adam Dunn to open the inning, then hit Dayan Viciedo with a pitch before walking Jordan Danks to load the bases.
Davidson followed with a two-run double and scored on Hector Gimenez's sacrifice fly to left.
"I thought he was good until he fell apart," Brewers manager Ron Roenicke said. "He was a little frustrated and just got a little out of whack mechanically."
White Sox starter Felipe Paulino had his best effort of the spring, striking out four while scattering three walks and two hits over five scoreless innings.
"He looked good," White Sox manager Robin Ventura said. "He threw fairly well. I just thought he was getting ahead. When you feel like you can throw strikes and you throw that hard, it's a little bit easier on you."
Richmond's homer came in the seventh off Brewers closer Jim Henderson.
Lohse wasn't overly concerned about his rocky outing.
"I just kind of got out of kilter for a minute and couldn't find everything I needed to but I got what I needed to," Lohse said. "It's spring. You don't want to go out there and (stink) but it doesn't mean as much when you're just trying to get your work in."
STILL HURTING, STILL PITCHING
Brewers right-hander Francisco Rodriguez still has a foot full of cactus spines, after stepping on one last week, but struck out two in a scoreless outing Monday and aims to be ready to go when the regular season gets underway March 31.
GARZA GETS WORK
Brewers right-hander Matt Garza was scheduled to pitch a minor league game Monday at Maryvale Baseball Park. Garza was pulled with two outs in the second inning of his last start. He threw 63 pitches over his six-inning start, allowing three runs -- two earned -- on six hits with five strikeouts.