I am potentially being sued by a tenant for leaving my apartment before the end of the lease, but the landlord is not interested in suing me.
Based on the information in your question, it seems unlikley that another tenant in the building could sustain a suit against you for leaving before your lease is up. First, the other tenant is not a party to the lease, therefore there is no basis for them to enforce the terms of the lease that run between you and the landlord. Second, I do not know how that tenant is damaged or harmed by your potential breach of the lease so what would they be seeking to recover from you? The other tenant may have some non-contractual reason for suing you (for instance, you have interfered with their use and enjoyment of their rented space), it is not clear how they are harmed by you leaving before the lease term expires.
Should you actually be sued, I would be happy to meet with you and discuss the case in more detail. Please be advised that my response is for informational purposes only based on the limited inforamtion you have provided. You should not construe such it as legal advice, and should consult with an attorney for advice on your specific legal issues.
Under most normal circumstances, another tenant in the building would not have standing to sue you for breaking the lease.
Without knowing all the facts, it's possible that the other tenant has some legitimate reasons for suing you, however.
Disclaimer: This answer is provided as a public service and as a general response to a general question, it is not meant, and should not be relied upon as specific legal advice, nor does it create an attorney-client relationship.