I'm not the river police, but I can reason some geography on your map. I prefer the first to the second.

The huge lake draining through the mountain range eastward is highly unlinkley. It makes your (island?) terrain tilted with high ground on NW and lower land over the whole south coast. The depicted mountains suggest otherwise. I think you could suggest that land is higher depicting high cliffs on the western coast, but the perspective won't make it easy (I guess the artists here could help on that, though)

As for option 1, it looks much more reasonable. The lake could form from the the runoff of all the rain on the east slopes of the range which accumulates in a mid-continent depression. This would be congruent with West->East maritime winds, which are typical northern hemisphere temperate climate, and also consistent with the overall mountain system. The lake would one outflow from a low point, probably the very end of the small mountain chain that runs south from the NE coast (you could continue it with some hills to make this more obvious). If you choose to go down this path, I would suggest adapting the shape of the lake into something more elongated, roughly respecting the shape of the western chain (roughly, a capital D).
Which also brings another subject - a detail if you like. If the majority of the rivers appear on the west slop, that means that's where the humid winds come from. Which means the east coast is in the "rain shadow" of that main range. Hence, your highly forested area should not be there. (Or, if that is highly forested, the west should be even more forested - if it's not, the main reason is human deforestation, aka, many people and lots of agriculture).

Hope this helps. The map looks good overall.