"Sarah Jane Smith" was her character. She was the last companion to Jon Pertwee's "Doctor" and the first companion to Tom Baker's. Anyone who ever watched Doctor Who likely considered Sarah Jane the Doctor's "first love" - though they never once had any romantic scenes they had a chemistry that made you suspect there were deeper feelings. Turns out that's because Lis Sladen was adored by the entire cast and crew at the BBC.
When she left the show the Doctor materialized the TARDIS to let her out, not on Hillview Road as planned (and probably not even in South Croydon) but on a grassy hill in the middle of nowhere. She takes it in stride and heads off hopefully to civilization whistling a tune. The fans only knew she eventually made it home thanks to the failed "K-9 and Company" spin-off pitched in the 80's. It never got picked up despite testing rather well - but I've seen the pilot episode and it's terrible, so I can only assume it garnered 8.4 million viewers because they wanted to see more of Lis Sladen as Sarah Jane Smith. Thankfully we don't have to remember her for that series.
In the new Doctor Who series they wanted to bring back one of the Doctor's old companions for an episode and there was no question it would be Sarah Jane Smith. She returned more than once to the role in the new series because the fans ate up every appearance. That lead to a deal with the CBBC (Childrens BBC) for her own spin-off series called the "Sarah Jane Adventures" reportedly one of the most popular kids' shows ever on the BBC.
Tom Baker wrote a wonderful tribute to her on his blog site recounting the first day he met her and how they immediately clicked. I always had this feeling that she was either a fantastic actress, or maybe she wasn't much of an actress at all and she was just playing herself. Turns out she wasn't far off from her character, which is probably why the fans felt she was so genuine. You just knew if you ever met her - either Sarah Smith or Lis Sladen - they were the same person and you'd instantly be friends with her. That's important when you're running for your life from Zygons I suppose. Her death took Tom Baker by surprise too - he had just signed a contract to do six new Doctor Who "audio drama" episodes with her at Big Finish.
The very first episode of Doctor Who I ever saw was "Pyramids of Mars" - which I regard as one of the best Tom Baker episodes ever made - and Sarah Jane was his companion in that. I know a lot of Whovians watch the show and wish they were from Gallifrey and had their own TARDIS. But the Doctor is such a big character - an alien, a genius, a hero - that those are big shoes to fill. Scary big. I found that, while I loved the Doctor, it was usually the companions with whom I identified. The companions were attainable role models - all they have to do is be who they are, have a sense for adventure, and when the TARDIS materializes a willingness to see what wonders the depth and breadth of time and space have to offer. Since Sarah Jane Smith so defined the role of a Timelord's traveling companion she became the yardstick by which I've measured all others.
I suppose that's why I always have considered her to be the "first" companion to the Doctor, even though I've since seen the earlier episodes in the series and know others came before her - but none could replace her.