“Partners” implies a partnership. Whether in writing or not, that’s a legal contract that is being created. If a written agreement exists, it needs to be reviewed by a lawyer, and be revised to include the new partner, including any new protection that the new partner and the remaining partner agree on.
If the property is currently owned by an existing partnership, than possibly nothing needs to be done with the deed. If the intent is for the property to be owned by a new partnership, then a new deed can be drawn in the name of the new partnership.
If I was the remaining partner, there is no chance I would agree to a lien in favor of the new partner, unless some of that cash is going to the remaining partner or the partnership. Ownership of the property essentially creates a lien. The owners own everything that is not protected by other liens. It’s unclear to me why a new partner would or should have any preferential position over the remaining partner.
Partnerships are only as reliable as the individual partners are. My father was in one for more than 30 years with no written agreement. I’ve been in one with a very simple written agreement since 1992 without any problems.