Liz is a new kind of companion, Describing her as a new member of the TARDIS crew is a bit off since she never actually gets into the TARDIS. She became a Dr Who sidekick during the period where the third doctor has been marooned on Earth with all his knowledge about Time Travel removed from his brain.
Liz hooked up with the doctor in "Spearhead from Space" to help UNIT defeat the Autons. She's a scientist, and she may have also thought she could learn something. When she left at the end of 'The Inferno", she reportedly told the Brigadier that all the Doctor really needed was someone to pass him his test tubes and tell him how brilliant he was, not what she was looking for.
Liz is played by Caroline John. She and/or the BBC ended her role as Liz is 1970. The BBC was said to have a problem with her in that she was too smart. They needed a dumb broad who asked a lot of silly questions. Then there was another issue of expanding importance that caused her exit, she was pregnant.