The first time I played Lone Survivor I only managed to get near the cat and talk to him. I didn’t click that I could gave him some cat food, that probably because I’ve had already eaten the cat food.
I did a second pass and I managed to get him to follow me in my apartment, little “Sunny” (That the name I gave him) really did make a difference my character mental health.
This cute little cat is near the hospital in the city. But before seeing the cat you need to get some cat food and the only way to get tin of cat food is to trade “Sleepy Cat comic” for them with the Director. I’ve found a total of 4 comics, they’re probably more but that should be enough to get the cat in your apartment.
Once you got cat food you can go see the cat nears the hospital. Approach him slowly, look the way the cat is moving when you are moving toward him. If he move stop going toward him and wait until he is acting normal again. Once you are near him talk to him and give him some cat food. He will then go away but don’t worry I’ll be back.
Now you need to go back to your apartment and take a nap. Once you wake up go outside your apartment (take the stair), he should be there and give him an another tin of cat food. Go back to your apartment again and he should be waiting for you at the fire escape window of your room. Just give him some food again and he will enter your apartment you will even be able to give him a name. I don’t actually recall what the 4 can did when I gave him, try it and you will see 🙂
Here a complete video on how to get him:
Update: Giving him a fourth can of food will give you the option to pet him.