Ryan Lavarnway’s second tour of the International League didn’t start out as smoothly his 2011 stint did, but the Red Sox catching prospect has been warming up in June with Triple-A Pawtucket.

The 24-year-old Lavarnway went 3-for-5 with a homer and two doubles for Pawtucket against Syracuse on Monday. It was Lavarnway’s sixth multi-hit effort out of 12 games this month, during which he’s hitting .360/.421/.720 in 50 at-bats. The homer, a fourth-inning solo shot off Syracuse righthander Yunesky Maya, was Lavarnway’s fourth of the month after he had just three in April and May combined.

After hitting .261 in April and .275 in May, Lavarnway’s improved his line to .291/.382/.462 for the year. His seven homers at roughly the halfway point of the season have him easily on pace for a career-low for a full season. He’s hit 21, 22 and then 34 homers last year between the minors and majors, but there is good news elsewhere. Lavarnway’s maintained his walks rate (12 percent of PAs) while improving his contact rate (struck out 21.3 percent of minor league PAs last year, 17.2 percent this year). If his power keeps coming on as it has in June, he’ll start building a case for another big league look, though the Red Sox have been getting solid production from the tandem of Jarrod Saltalamacchia and Kelly Shoppach.