Perhaps the closest to the "authentic" evidence of Lambert's fate is presented in the Sigourney Weaver screen test before the actual shooting of the film on July 3, 1978. In the link's video
at 7:50, Dallas tells Ripley what the Alien did to Lambert.
Of course, this is not the final statement of Lambert's fate, it is the content of the early 1978 drafts of the script, although it does give an indication of what was planned for Lambert's death.