Who composed Lucasta: Postume Poems, published posthumously?

The correct option is Richard Lovelace.

Here is a step-by-step explanation of the historical and literary context of this work:

1. Who was Richard Lovelace?
Richard Lovelace (1617-1657) was an English poet of the seventeenth century. He is celebrated as one of the prominent Cavalier poets, a group of writers who supported King Charles I during the English Civil War.

2. The Origin of "Lucasta"
Lovelace's lyric poems were frequently dedicated to a lady whom he called "Lucasta" (a poetic blending of the Latin words Lux Casta, meaning "Chaste Light"). The first collection of these poems was published during his lifetime in 1649.

3. Posthumous Publication
Lovelace died in 1657. Two years later, in 1659, his brother Dudley Posthumus Lovelace compiled his remaining unpublished verses and published them in a volume titled Lucasta: Postume Poems. Thus, Richard Lovelace is the composer of the poems contained in this posthumous collection.