Synthases vs Lyases - nomenclature
Enzymes always catalyze reactions in both directions (all catalysts do). When an enzyme is first discovered and named, it is not always clear which direction is physiologically relevant (and sometimes both are).

There is a nice answer on StackExchange Biology talking about the enzyme pyruvate kinase, which acts as a phosphatase (i.e. in the opposite direction than the name suggests) in glycolysis. In the lab, you can study the reaction in both directions, depending on the concentrations of species present.

For the class of enzymes you are talking about, the same idea applies. A lyase can work in the other direction, as a synthase, and vice versa. If you want to classify enzymes in terms of mechanism and structure, there is no reason to separate the lyases from the synthases. They are expected to be highly similar or identical (if we are just using two names for the same enzyme).