I do not see how you expected the LL to "let you know that there would be a problem with this later on" as there would be no way to predict all the possible problems that would arise with the situation. For instance, if your fridge had a faulty cord and started a fire that burned the apartment complex to the ground the LL's insurance would come after your insurance to pay for the damage. If it was the LL's fridge that started the fire the insurance would handle it differently. If your fridge was too heavy and damaged the floor, you would be responsible, conversly the LL is responsible for all of his property and the damage caused.

In your post you say the the LL's fridge "was not working properly" this could mean many things. It was still functioning, right? The LL had no obligation to supply you with a new and better fridge. You do not say exactly what was wrong with it. Did it not keep the ice cream solid? It froze the lettuce? Was if just too noisy?

You bought one on your own and still have the one that was supplied with the apartment. The one you own is yours and the LL has no more right to touch it than he would anything else that you owned like your televison set or computer. How would you feel if the LL came in and decided to paint your fridge blue? He could only do that with one he owned not one you owned. He could decide to repair your fridge out of goodwill but what if you were not happy with the repairs he made and decided to sue him? He probably does not want to take that chance.

The LL is not going to repair/replace your refigerator that you would be taking with you when you move. The only possible solution is to negotiate the LL to repair/replace the fridge that he owns and is part of the rental unit that is still there.