I think we're looking for artists who never made recordings after 1948 when vinyl microgroove records first appeared.
From 1948 until around 1959 a lot of new recordings were issued on vinyl and shellac, or on vinyl only while 78's were phased out, just like they did when CD's took over from LP's and singles, and DVD's took over from VHS.
The bulk of Julie Andrews recordings were pressed in vinyl and were never issued until well after shellac had stopped being used by the record industry.
There's still quite a few artists alive that fall into this same category, like Petula Clark as already mentioned, and Shirley Bassey, who in my opinion put on the best live performance I've ever seen in my life. Way better than even Petula Clark, Madonna or Kylie, all of which I've seen and loved.
Mary Lee seems to be the only one still living so far, who never made a recording during the vinyl years.