The moves were made Friday.
Lavarnway appeared in 97 games with the Red Sox from 2011-14, and he also played seven seasons in the team's minor-league club. Last season, when he was limited by a strained left wrist he hit .285 with a .389 on-base percentage, four home runs and 24 RBIs in 67 combined minor league games while also appearing in nine games with Boston.
The 27-year-old catcher is from nearby Burbank.
Butera appeared in 61 games with the Dodgers last season and played in 65 total games with the club after he was acquired from Minnesota at the 2013 trade deadline in exchange for Miguel Sulbaran.