No, you can't sue for this reason.1) If you don't have a written employment contract, you can be terminated--and therefore lose the apartment--for any reason whatsoever, at anytime, because without a contract, you are an "employee at will." The employer/landlord can just decide to fire you because they no longer want you, and that is their right.2) Putting your own money into an apartment or property doesn't give you any rights to it or to reimbursement/compensation unless--and only if--there was a contract for you to do this in exchange for getting something, and the landlord breached or violated the contract. If that were the case, however, you could sue the landlord for breach of contract, to enforce its terms in court.