Fujinami, 29, is in his first major league season after playing for the Hanshin Tigers of Japan's Nippon Professional Baseball from 2013 to 2022.
In 34 appearances (seven starts) with the Athletics, Fujinami went 5-8 with an 8.57 ERA across 49⅓ innings. He most recently pitched against the Boston Red Sox on Tuesday, surrendering a hit in one inning of scoreless relief.
Lucas, 26, has yet to make his big league debut. In 21 relief appearances between Double-A Bowie and Triple-A Norfolk this season, Lucas went 1-0 with a 2.93 ERA.
Oakland made the deal shortly after beating the Red Sox 6-5 on Wednesday to take two of three games in the series.