Lovelace wrote a rather large number of poems about Lucasta, and he even titled one of his collections of poetry Lucasta (1649). And it's not like Lucasta is the most common of names. So if you're reading a 17th-century lyric about a lady named Lucasta, it's a safe, nay, sure bet that you're reading Lovelace.
Some of the other poems about Lucasta are: "To Lucasta, Going Beyond the Seas," "To Lucasta, from Prison," "Ode to Lucasta, the Rose," "Dialogue: Lucasta, Alexis," "Lucasta's Fan," and "Lucasta, Taking the Waters at Tunbridge." Just to name a few.