It depends on the size of the room, how many lions there were and how healthy they were to being with.

Lions can typically survive for two or more weeks without food, so it unlikely that all of the lions originally in the room remain. It is likely that the weakest lions will have died of hunger, or been killed by the stronger animals and eaten, sustaining the remaining animals, but reducing the total number of lions.  A lion typically eats up to 50kg of meat at a time after a week of not eating, or 10kg per day when in captivity.  A typical lion weighs between 150kg and 250kg and so it can be assumed that one lion could sustain twenty others a day, or four per week.

For a lion remain after 3 months, there must have been at least 7 lions in the room initially, however lions are highly territorial and would be unlikely to tolerate a large number of other lions within a confined space, and so it is also likely that there would have been early territorial fights, reducing the number of surviving lions.  Increasing the number of lions in a confined space would increase the chance of survival, but would also increase increase the chance of territorial fighting.

Depending on the size of the room, it is very unlikely that even a sizable population of lions without any other food sources would survive to pose a danger, and if the room was large enough to avoid territorial fighting, it may be large enough for the person to survive by avoiding the hungry remaining lions, until they too perish.
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