Wrong on all points. Iran has already used anti-ship ballistic missiles. They might not be as advanced as China's but they appear to work, and in confined areas the targeting can be done using mobile shore-based radars.

https://warontherocks.com/irans-anti-access-and-area-denial-...

Even setting the ballistic missile threat aside, LCS can't defend itself against regular drones and cruise missiles. It's severely limited in terms of sensors, fire control, and magazine depth. In order to operate in that area with reasonable survivability it would have to be escorted by a more capable surface warship with area air defense.