Sign out, and just sign in with your new account. Do this in the Creative Cloud desktop app, or you can do it in LR. LR will then be authorised with your new personal account.
But first, make sure anything you have uploaded to LrMobile from a phone or wherever is synced down into your Classic catalogue and is on your hard drive. Stuff in the cloud is linked to the account, so it'll be linked to the work account and will be deleted by Adobe after (I think) a year. So download it now.