how can i find passenger lists from the Queen Elizabeth from the 1950's?

Answer 1

After checking the Internet, I do not think there is any compilation that includes all of the 1950s.

Try this site:

http://www.oceanliner.com/passlist.htm

Answer 2

Ancestry.com has an immigration collection with ship manifests up to 1957 (for at least those arriving at NY and California). You can look at Ancestry in most public libraries for free.