Had an idea for a medieval fantasy world but need a little help with geography and climate.

Hey guys, been a fan of fantasy worldbuilding for maybe 10 or 15 years. I've always been fascinated with medieval fantasy but I've always built my worlds with magic. I've been getting ready to start a story that I want to be set in a medieval setting without magic. I've had an idea but need a little bit of help with the geography and climate of the region. I've got a rough idea of what I want to happen but need to know if it's realistic. <br><br>I want this story to be set solely on an island. An island that's roughly the size of Greenland. I don't want a sea or ocean to be involved. Instead I want a massive freshwater lake to be part of its surroundings. I know that a lake large enough to surround a massive island like that would need to be fed by multiple rivers and streams. I would want the lake to be fairly shallow. I don't want it to be like the great lakes. I'd prefer it to be like a big, wide lake that's only maybe 100 ft at its deepest point. As for the island itself, I'm looking at something with a mountain range down the middle. One side of the mountain range would have a series of rivers that lead into the lake. The other side would have no rivers but would have a number of waterfalls leading into the lake. I would also want one side to be more inhabitable than the other, one side fairly lush and forested and the other more barren. One side would also have a few ports. The other side of the island would have one port. <br><br>Does this sound possible? Any thoughts or opinions on this? If I'm being completely unrealistic with my ideas, please let me know. I appreciate any and all feedback. Thanks.<br><br>Edit: Take a look at my comment below, I put a picture of Oceania in there. I think an island similar to that is what I'm looking for.