Lonnie Byers is the father of Will and Jonathan Byers. He was previously married to Joyce, and when they got divorced he didn't make much effort to keep in contact or try to keep a healthy relationship with his sons, caring more about his girlfriends.
When Will goes missing, Joyce calls him multiple times, not because she believed in the possibility of Will being with him, but because Chief Hopper did. He never answers his phone, but his girlfriend does, and hang up on her once she acknowledges it's his ex-wife.
Jonathan then goes to his house looking for his little brother. Lonnie doesn't care much that Will is missing and just puts the blame on Joyce.
In "The Flea and the Acrobat", his eldest son comes home to find he's gonna crash in their couch for a few days, and his mom believing he was there because of Will's funeral. Joyce later finds out he's not there because of the funeral, but because he wants to take money off of Sattler, the company that owns the quarry that it's believe Will fell into and drowned. Joyce then kicks him off and he doesn't appear again for the rest of the season.