There are two Delta Airlines Delta Sky Clubs at LaGuardia.
The first one is located in Delta Terminal at concourse level, after security, just before Gate 2. Opening hours: Sun-Fri: 5am-10pm, Sat: 5am-7:30pm. No shower.
The second one is behind the Delta ticket counter adjacent to security checkpoint. Sun-Fri: 6am-7:30pm, Sat: 8:30am-6:30pm. Must be 21 to get in this lounge, or be with a legal parent over 21 who also is a club member.
See here for number of guests allowed, depending on one’s membership program