Milwaukee overcame two home runs by Dominic Brown, including a three-run blast that put the Phillies ahead in the first inning. Brown hit 12 home runs in the month of May, giving him 15 for the season.
Lucroy doubled home a run in a two-run second that brought the Brewers within one and they took the lead for good with four more in the third.
Lucroy had an RBI single in the third and he hit solo homers in both the fifth and ninth innings.
All of that helped Milwaukee end a six-game losing streak, its longest of the year. The big offensive night allowed Yovani Gallardo (4-5) to pick up the win even though he allowed five runs on six hits in 5 2/3.
Cole Hamels (1-9) endured another rough start to take the loss, surrendering seven runs on 12 hits in five frames. Hamels went 0-6 in May with an ERA of 4.95.