Liz is related to Laura/Leslie Webber by marriage only - it's sort of hard to explain but I'll give it a try
There was a woman named Helene Webber she had two sons Rick and Jeff, both doctors. Eventually we found out that Rick and Jeff were only half brothers, they did not have the same father. Jeff's father was actually Dr. Steve Hardy. But since he didn't find this out until he was full grown he kept the name Webber out of respect for his mother and the man who raised him.
Rick married Dr. Leslie (Faulkner), eventually she learned that a child she thought had died at birth, had actually be put up for adoption by her father. She and the child, Laura Vining eventually reunited and Rick adpoted the 16 year old girl, thus changing her to Laura Webber.
Jeff left the show and was not heard from again until his oldest daughter Sarah came to town to live with Grandma Audrey when her parents moved to Bosnia. Younger sister, Liz arrived shortly there after.
So through marriage Laura and Liz are actually cousins - sort of!
(Does that make her Nik, Lucky, & Lulu's aunt????)