The runway star, who does not have kids, is all dressed up as a mother at a glamorous restaurant in the provocative Equinox commercial, in which her halter neck dress is pulled open to allow the babies to feed from 'mum's' bare boobs.

The promo, one of a variety shot by renowned photographer Steven Klein, features the company's slogan, "Commit to Something", slapped across the image.

"Equinox is about commitment - we are obsessed with it, and we challenge our members to know who they are and what they want," states Carlos Becil, Equinox Chief Marketing Officer. "The concept of commitment is bold, incredibly powerful, and it's real, especially in a world today where commitment is lacking."

However, the bold and bizarre commercial has drawn mixed reactions from people online.

"Disgusting on two levels," one critic writes on Lydia's official Facebook page. "1. no one wants to lose their appetite at dinner by seeing breastfeeding and boobs not being covered up (gross)... it takes away the rights of other diners, 2. They aren't even her kids (gross)... and furthermore, I breastfed... but I excused myself or covered up... WHY do some women think that their right to breastfeed in public means that they have to whip out an entirely naked boob just to make a point WHY?"

Breastfeeding advocates have welcomed the ad, with many applauding the ad concept, including officials at the La Leche League of New York.

"My initial reaction is, 'Great, let's normalise breastfeeding'," representative Leigh Anne O'Connor tells FOX411. "Of course, the image more glamorises the situation but I don't have a problem with that because breast feeding is an everyday thing that is done at home in pyjamas, out at weddings or movie theatres or restaurants, both fancy and low key."

"I do not believe the breast is sexually used here," she adds. "When critics call it disgusting to breastfeed in public or in ads, I say that is a personal issue with the critics; they are uncomfortable with their own bodies and are projecting their feelings on others."

Hearst, who became engaged to comedian Chris Hardwick in September (15), has yet to comment on the backlash.