Is it possible that my lift pump could drain a sink trap empty. The sink and a dishwaher are located in the basement between the lift station and the septic tank. Both are not as frequently used as the downstairs bathroom. If this is the case, is there an air vent that can be attached to the sink that would draw air through it instead of the sink drain when the toilet is flushed

Yes the pump can suck out your trap if your vent stack is clogged. Adding a Studor vent, AAV, would prevent the problem but rodding out the vent is what should be done.