If you zoom in on Karakorum you should be able to see the lighthouse in the Lake. You might have to move the view angle around. I can't see your screenshot to say for sure.
God Emperor answered this question not so long ago in the newbie thread. All praise and spice to him:
There is also a size requirement for the body of water in order to build various things
Any body of water under 10 plots in size is a freshwater lake and you can not build much of anything for such a small body of water (which is not so small).
There is also a size 20 requirement for some things.
This makes seas of size 10-19 be in a sort of indeterminate zone where you can build some things but not everything.
A lighthouse (or Viking Trading Post, Carthaginian Cothon) only requires 10, a Customs House (or Portuguese Feitora) also needs only 10
The Great Lighthouse needs 10, as do The Colossus and Moai Statues
A drydock requires 20
Ships (galley, trireme, etc.) need size 20. Except Workboats which have no specific size requirement but are the only unit with the "bPrereqBonuses" flag set so you should not be able to build them if the body of water has no resources in it.
That may or may not clear things up...