Hello and thank you for the opportunity to assist you. My name is ***** ***** I will do my very best to answer your legal questions.
It could go either way if you were to sue. The question is whether they implicitly agreed to take responsibility for the sweater. Their answer, obviously, will be that they did not, and that all they did was agree to place it in their lost & found pile. Moreover, they will likely argue that you were negligent in leaving the sweater in the first place, and negligent against for not picking it up immediately after calling the bowling alley or even the next day.
Your response, of course, can be that the employee promised to make sure that nobody, except you, was able to take the sweater, and therefore, the bowling alley was negligent. As mentioned above, it could go either way in court depending on how well each case is presented, and the judge's own opinions about the matter. I do think that you have a decent shot at winning, however.
Does that answer your question? Please let me know if you need clarification, as I am happy to continue helping you until you are satisfied.