Answer and Explanation:
A comma splice is the use of a comma alone to join sentences that were originally independent. It is a common mistake, but it should be avoided. Notice how that happens in sentence 1:
Lucia walks on the beach every morning, today she saw two turtles headed for the ocean.
Notice how the comma breaks the sentence in a strange manner. One way to correct that would be by adding the conjunctions "and" or "but" after the comma.
A fused sentence happens when we put together two independent clauses with no punctuation or conjunction to connect them at all. That is what happens in sentence 3:
Lena joined Lucia the next day she was hoping the turtles would appear again.
This can be correct by adding a semicolon or a comma plus a conjunction.
Sentences 2 and 4 are correct as they are. They use commas and conjunctions to connect the independent sentences:
Lucia loves turtles, and she invited her friend Lena to walk with her.
The girls didn't see any turtles, but they did see a leaping dolphin.