I have noticed on a couple of occasions that a hazard had no visible stakes/markers to identify as lateral or otherwise. What is the proper "assumption"?

A Lateral Hazard runs alongside the playing area, which usually makes it not possible to drop keeping point of entry between you and the hole.

A Water Hazard runs across the playing area.

What do you do if it runs both along side the fairway and across the playing area? Once it gets into the playing area you drop behind (even if it is not water, per se)?

A water hazard can be lateral at one point and direct at another. If it were marked, it would have a red stake with a yellow stake right next to it, identifying where the lateral ends ( or starts ) and the direct begins (or ends ).
Easy rule, if you can't drop your ball with the point of entry between you and the hole, it's lateral.