The notable thing 68-year-old Lauda and octogenarian Ecclestone do have in common is their accumulation of birthday candles.
A joint statement from governing body the FIA and the F1 Group said the choice would be made "on merit or by lottery".
"Over the previous year we have looked at a number of areas which we felt needed updating so as to be more in tune with our vision for this great sport", said Sean Bratches, Managing Director, Commercial Operations at Formula 1.
She said her stints as a grid girl and spot on Top Gear paved the way for more modelling assignments.
FIRSTHAND ACCOUNT: AUTOWEEK published a Q&A with British grid girl Samantha Young "to get the feelings of someone now down a job for the year". "Formula E stopped using grid girls past year already, but we just didn't feel the need to shout about it", a spokesperson from Formula E said.
Bratches said the practice was not "appropriate or relevant to Formula 1 and its fans, old and new, across the world". "They could have looked at making it more equal between the sexes in the role". If a company relies heavily on pretty women promoting them, then maybe they need to rethink their brand.
Our favourite images of the super blue blood moon A lunar eclipse of a full blue moon is seen above a statue at the Chhatrapati Shivaji Terminus railway station in Mumbai, India. According to NASA, the moon will be 223,068 miles from the Earth tonight, nearly 15,000 miles closer than average.
I'm quite conservative and paternalistic and I'm not repulsed by that logic, except it seems odd to use it in this case.
"This is an important discussion and it should not be oversimplified or trivialized. I feel that it shouldn't be "all or nothing" but instead an equal opportunity for men and women to enter into Motorsport in the manner that they choose". "So this is a decision against women".
Former Williams F1 test driver Susie Wolff told BBC Sport the deployment of grid girls did not offend her, and that F1 had more pertinent issues regarding the involvement of women in the sport.
Grid girls are hired to carry out promotional work at the F1 and wear clothes representing the sponsors of the event.
Fellow grid girl Rebecca Cooper wrote on Twitter: "Ridiculous that women who say they are "fighting for women's rights" are saying what others should and shouldn't do, stopping us from doing a job we love and are proud to do".
"We're using a new concept and focusing on grid kids, and where possible we involve young and aspiring drivers that race in junior go-kart championships".