She actually may need to involve lawyers in both states. She will need an attorney in New Jersey to make sure the real estate transfer is appropriate and there are no tax issues or other traps for the unwary. She will also need an attorney in California to make sure the trust satisfies California law, especially if she is hoping to protect the house in case she needs MediCal (i.e. Medicaid) someday. Start with a California attorney and then enlist a New Jersey one to review the trust and transfer the property into it.
This guidance may hold true when moving from any state to another. Again, consultation with an attorney is recommended.
To find an attorney, go here: https://www.elderlawanswers.com/elder-law-attorneys