Lithely is how someone moves when their body is lithe: easily, smoothly, with grace, not in a stiff or clumsy way. It is simply the adverb of lithe. The word belongs more to stories and sports writing than to ordinary talk. “She slipped lithely through the crowd” paints a picture; almost nobody says it when they ask you to pass the soy sauce. Use it when the movement itself is the point — climbing, landing, sliding into a seat — not as a fancy extra on every verb.