WIP - basic elevation map

[Pixie]

You don't really need a lower than sea level depression to have a lake. It very much depends on the climate around your area.

If it is a rainy/temperate area, a lower than sea level region would fill up and eventually create a flow towards the sea. The Great Lakes in Canada/US and Lake Victoria in Tanzania/Kenya are good examples of this (hell, the Nile is what flows out of Lake Victoria!).
Only if the climate is dry enough will evaporation equal/top the influx of water and prevent any lake from overflowing.

Depending on the size of your lake, you should consider a bottleneck of hard rock which limits the outflow. This is exactly what creates a lake.
In the case of your map, I'd squeeze the northen mountains a little together, so you can have just that.
If you make them sufficiently close, you can have a sort of a gorge that the lake has eroded. A good example on Earth of such a gorge is the Iron Gates in the Danube. Check this picture:
http://donsmaps.com/images8/djerdap.jpg

Also, looking at your map, you can have a series of interconnected lakes (the dark green). But this would require, imho, a finer topography (more elevation level).

And lastly, with a little more detail added, consider saving a B&W version (black being sea level) and fiddle with it using Wilbur.