Let's start with this:
Lay and lie are often confused. Lay is most commonly a transitive verb and takes an object. Its forms are regular. If “place”
or “put” can be substituted in a sentence, a form of lay is called
for: Lay the folders on the desk. The mason is laying brick. She
laid the baby in the crib. Lay also has many intransitive senses, among them “to lay eggs” ( The hens have stopped laying), and it
forms many phrasal verbs, such as lay off “to dismiss (from
employment)” or “to stop annoying or teasing” and lay over “to make
Lie, with the overall senses “to be in a horizontal position, recline” and “to rest, remain, be situated, etc.,” is intransitive and
takes no object. Its forms are irregular; its past tense form is
identical with the present tense or infinitive form of lay: Lie
down, children. Abandoned cars were lying along the road. The dog
lay in the shade and watched the kittens play. The folders have lain on the desk since yesterday.
In all but the most careful, formal speech, forms of lay are
commonly heard in senses normally associated with lie. In edited
written English such uses of lay are rare and are usually considered
nonstandard: Lay down, children. The dog laid in the shade.
Abandoned cars were laying along the road. The folders have laid
on the desk since yesterday.
I wanted to highlight all the confusion that exists between definitions of lay and definitions of lie. Lay can be a tense of lie but lay can also be its own verb. In this case, lay is being used as a transitive verb and takes an object and the object is the phrase out. One could also describe that phrase as out [there] where [there] is understood. A definition of lay is:
to place, set, or locate:
The scene is laid in France.
It is also important to note that lay is a common word in nautical usage and the definition of lay for nautical usage is also relevant
Nautical. to move or turn (a sailing vessel) into a certain position
In this case, the Hispaniola is both sitting some way out and also there is a need to lay a course to the Hispaniola. The use of the word lay is intended to invoke both connotations at once. The word lay is also intended to invoke common language of seamen, so as these nautical words come up in the narration the reader has a feeling of being there, in the boat, with sailors speaking language of the sea.