Elizabeth Willis might have been a descendant of John Willis of Bridgewater, as some lines of his descendants went to Bristol Co. The major problem with northern Bristol Co. families is that so many of them came through Taunton, which has been a black hole for genealogists due to the destruction of the town records in the 1838 fire.
Offhand I don't see a connection to any of the Holmes lines which I have explored, which is to be expected since most of them are from John the messenger.
I have checked some other sources at my disposal but have not found anything which might illuminate your search.
Dale H. Cook, Member, NEHGS and MA Society of Mayflower Descendants; Plymouth Co. MA Coordinator for the USGenWeb Project Administrator of http://plymouthcolony.nethttp://plymouthcolony.net