From the "Solo Traveler" patent:
A more specific object of the present invention is to provide a lid having an opening formed therethrough to enable drinking, and having a recess formed in the lid adjacent the opening to accommodate the upper lip of one drinking from the cup
This is also illustrated in the patent diagrams.
I came across this interesting article on the history, use, design, and styles of disposable lids. The Solo Traveler is prominently featured for its excellent aesthetics and design . The article reiterates that:
the Solo Traveler lid was designed to accommodate the nose and lip of a drinker. In accomplishing this design goal, the necessary height of the lid made it useful for foam-topped gourmet coffees.
Additionally, when upright, the recess acts as a reservoir (complete with drainhole) to catch drips/spills/splashes that might otherwise run down the cup and create the infamous coffee stain ring.