According to skysports, Chelsea appoints Lampard as an interim manager until the end of the season. So, it is clear that Lampard only manages Chelsea until this season is over. But he may be considered to continue managing Chelsea in the next season if Lampard makes Chelsea management satisfied. But I doubt that Lampard will get the chance since there are still 4 big remaining matches for Chelsea. Lampard may get losses in these matches, and Chelsea management won't consider hiring him as head coach for the next season.

https://www.skysports.com/football/news/11668/12850853/frank-lampard-chelsea-appoint-former-manager-as-caretaker-manager-until-end-of-season#:~:text=Frank%20Lampard%20%2D%20April%20to%20May,managers%20during%20his%20playing%20days.