Lainez, 20, has struggled for game time at Betis, starting just two of his 14 La Liga appearances this season.
And Lyon have asked about his situation after previously contacting Betis in December 2019.
During the winter, both Lainez and Betis staff decided he would stay until the end of the 2019-20 season.
However, with his situation not improving Lyon have returned and could sign Lainez on loan or permanently.
Lyon and Betis have a good relationship after OL sold Nabil Fekir and his brother Yassin to Betis last year.
The Ligue 1 side must wait for a decision from new coach Manuel Pellegrini and the incoming sporting director, likely to be Antonio Cordón.