James Cutfield, a 51-year old New Zealand national, was put under investigation on Monday (local time) by Italian prosecutors.
"The captain exercised his right to remain silent for two fundamental reasons," lawyer Giovanni Rizzuti told reporters.
"First, he's very worn out. Second, we were appointed only on Monday and for a thorough and correct defence case we need to acquire a set of data that at the moment we don't have."
Lynch and six other people were killed when the British-flagged Bayesian, a 56m-long yacht, capsized and sank on August 19 within minutes of being hit by a pre-dawn storm while anchored off northern Sicily.
Being placed under investigation in Italy does not imply guilt and does not mean formal charges will necessarily follow. It is still unclear whether other crew members or other people will also be placed under investigation.
Prosecutors said their investigation would take time, and would require the wreck to be salvaged from the sea. The Bayesian is currently lying on its right side, at a depth of about 50m.
The coastguard is conducting activities to monitor the environmental conditions in the area where the yacht sank, it said in a statement.
"At the moment we don't register any leaks from tanks and there are no traces of oil pollution," it said.
