To the best of my knowledge:
One person can enter multiple applications, specifying up to 15 entry dates on each application. Each application costs $6. During the lottery processing, as soon as the first processed application successfully awards any one of the 15 entry dates for the number of hikers specified, ALL other applications for that individual are automatically cancelled.

If a second person in the same group signs up and submit entries for a trip, and if one of their entries is successful, then the second trip is awarded. However, Inyo staff will try to identify these situations and cancel one of the awarded trips. They do this so that more groups have a chance of scheduling a trip. (I am not sure how two people are tied together to the same group and trip.) It would be especially kind of the people in the multiply-awarded setups (who are not identified and canceled), to immediately decline one of the trips online so others can get a permit.

I think two people submitting separate entries for the same trip gives you no better chances of winning than if one person submits all the entries. The odds of winning a trip are just the same.