Star Trek and LIS are only similar in that they are two shows that take place in space. And for the first two seasons, LIS spent most of the time on a single planet set.
Now if you're gonna compare Star Trek to an Irwin Allen show, then go with Voyage to the Bottom of the Sea. Voyage detailed the adventures of a paramilitary ship out on missions of peace, battling aliens, crazy people, ruthless leaders, and so on. The show developed into a Big Three cast (Nelson, Crane, Sharkey), an almost regular lead character (Chip Morton - downgraded when Sharkey came along) with prominent supporting characters with no first names (Kowalski, Patterson - Sulu, Uhura).
In fact, even NBC felt the two series were similar and asked the production staff to "be more like Voyage" to save money since the budget was apparently lower than Star Trek, according to memos reproduced in, I believe, David Alexander's "Star Trek Creator: The Authorized Biography of Gene Roddenberry."