Parker played the role of "Laura Banner" in the opening sequence of the pilot for the television series The Incredible Hulk (1977), and the fashion model-witch "Madelaine" in the Kolchak: The Night Stalker episode "The Trevi Collection".

Her other television work includes appearances on Emergency "One of Those Days"(1975-S5Ep8), Kung Fu, The Six Million Dollar Man (1976-S3Ep17: "The Secret of Bigfoot Part 1"), Police Woman, Kojak, Alice, Quincy, M.E., Hawaii Five-O, The Rockford Files, Highway to Heaven, Switch, Baretta, Galactica 1980 ("The Night The Cylons Landed", Parts I & II), Barnaby Jones (1980-The Price of Anger), the CBS daytime serial Capitol, and the ABC daytime serial One Life to Live.

[2] She appeared opposite Robert De Niro in the 1970 Brian De Palma film Hi, Mom!, but her best known film role came in the Oscar-winning drama Save the Tiger (1973), starring Jack Lemmon, in which she played a sympathetic prostitute who is devastated when her client suffers a near fatal heart attack.

Parker made her Broadway debut in 1968 in Woman is My Idea, written and directed by Don C. Liljenquist.

Later she was reunited with her Dark Shadows co-stars Jerry Lacy and Kathryn Leigh Scott in two feature films about Doctor Mabuse written and directed by Ansel Faraj.

At Vassar, she began a major in philosophy, which she completed at Southwestern at Memphis (now Rhodes College), receiving her BA.

After retiring from acting, Lara became a high school and English teacher and obtained her MFA in creative writing from Antioch University.