Kimolos is the small, sleepy neighbour of Milos: one village, a handful of beaches, pale chalky cliffs and almost none of the traffic of its famous neighbour. Leaving it for Lavrio makes sense if your trip ends at Athens airport or in the east of Attica, because Lavrio lands you far closer to the airport than Piraeus does.
The honest thing to know first is that this is a seasonal link. Ferryhopper's schedule data for this direction showed only Magic Sea Ferries, only between May and September, on 4 to 7 days a week. The same page's travel tips say there is no direct return from Kimolos to Lavrio at all, which tells you the service is not a fixed year-round line. Our older route data, which listed Blue Star Ferries on this direction, is not supported by Ferryhopper's more recent figures.
When the summer boat runs, it is a practical trip of about 4 hours on a conventional ship, which is quick for a crossing from the far western Cyclades to Attica. It saves you the longer journey into central Athens that a Piraeus arrival involves.
Before you plan around it, search your exact date. If nothing shows, the fallback is well trodden: Kimolos has sailings to Piraeus on 3 to 7 days a week all year, and Milos, a short hop away, has more connections still.