The poem's title pretty much sums up what happens in the poem: the speaker says adios to his honey (whose name is Lucasta) and heads off to the battlefield, hat in hand… sort of.
Based on what we know about ol' Lovelace, we think it's likely that the "wars" to which our speaker is headed refers to either the English Civil War, or to some military skirmishes in which Lovelace participated way back in the 17th century. But here's the thing: what wars we're talking about doesn't matter much here. It's war in general that gets our speaker's blood flowing.
Now, as for Lucasta: nobody is quite sure who she was, but some scholars speculate that she was a woman named Lucy Sacheverell, a woman with whom Lovelace was romantically involved; according to one story, she once feared that Lovelace had been killed in battle and married someone else. Ouch.
Whether or not this is true, the name Lucasta means either "chaste light" or "pure light." It comes from two Latin words, lux ("light") and castus/casta ("chaste"). By calling the woman in the poem Lucasta (who appears in a number of other Lovelace poems and which was also the title of a volume of poems he published in 1649), Lovelace represents her as a kind of pure, heavenly angel, and one that is, importantly, not a sexual figure. Frankly, it sounds like our speaker's love for Lucasta is a special, almost holy kind of love.