We introduce an incremental extension of the lazy grounding answer set solver Alpha. Unlike traditional systems such as iclingo and I-DLV, which combine incremental solving with full grounding, our ap- proach retains the advantages of lazy grounding (viz., reduced grounding effort) and enables multi-shot solving for problems where the ground- and-solve approach is infeasible. A Python prototype shows reduced grounding times and hence faster solving on dynamic 3-coloring bench- marks. This establishes the first step toward integrating incremental solv- ing into lazy grounding, addressing scalability in evolving domains.