Red and green sidelights are only used when underway- never while anchored. using them when anchored would invite a collision, especially with a vessel under 50m.
Rather than scan the applicable page from my copy of the rules, I googled and found this handy study aid:
https://www.google.com/search?q=72+colregs+rules+of+the+road&client=safari&hl=en-us&prmd=isvn&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjXg5iP2tzdAhWpnuAKHfdtArAQ_AUIESgB&biw=768&bih=922#imgrc=NX9-Y4pduKl46M:
Regarding anchor lights— the rules require a 360 degree white anchor light for vessels under 50 meters long. Vessels over 50m are required to have two such lights- one forward and one aft, and the aft one should be lower. The LV-112 (Nantucket) was 147’ LOA, so two lights aren’t required. But two lights are optional for shorter vessels, and I’m pretty sure Nantucket has two. One is on top of the jackstaff at the bow, and the other is on top of the flagstaff at the stern. (I don’t think the Lindberg includes these?)
I never served on a Lightship, but a Lightship sailor I know said they always had the proper lights and dayshapeMwhen anchored on station. I sure that was done service-wide - no CO would risk being found partially at fault for a collision bec his command wasn’t following the rules.
One reason lightships were hit or endured many close calls (esp. in the pre-radar days) was because ships would home in on the Lightship’s radio beacon in the fog, where lights didn’t really matter.
-Bill