As an island off the coast of Italy, Sicily did not have any major interactions with the Spartans before the Sicilian Expedition because the Spartans preferred to stay as close to Sparta as possible. However, the people of Syracuse, the biggest and most powerful state on the island of Sicily, were of Doric origins, which was something they had in common with the Spartans. Athens wanted Sicily because they viewed it as a threat; if the Sicilians gave their help to the Peloponnesians, it would be disastrous for the Athenian side of the war.
Their expedition to conquer the island was overall not successful for multiple reasons (such as the uncertainty about the expedition in the first place and its main supporter being recalled to Athens for a trial), but they did have some victories at the beginning. Syracuse did not react to the Athenian invasion, which led them to almost be conquered before the Spartan general Gylippus arrived and forced the to react.
The Sicilians were not involved with the Spartans before the Peloponnesian War, but because of the attack by the Athenians, they gained Sparta as a new ally, along with Sparta's other allies.