Problem
Julian phones his friend Liza to ask if she would look after his house for the next 2 years, since he is taking up a position at a New York firm. He explains that he will take all his furniture and household goods with him. Liza tells Julian that she likes the prospect of living in Julian's house with its leafy garden and coincidentally, the timing would work because her apartment lease is about to end soon unless she chooses to renew the lease. However she hates the idea of moving all her furniture, so she politely declines. Julian then throws in something to sweeten the deal, telling her that he could leave 'Betsy' the barbeque behind for her to use while she lives in the house. 'Betsy' is a huge barbeque with many special features. In the past Liza has enjoyed spectacular barbeque parties at Julian's house with their mutual friends, and Julian knows how fond Liza is of 'Betsy'. Liza and Julian sign a written contract which specifies that she can live in the house for 2 years in exchange for her paying the costs of electricity and gas, and for keeping Julian's house in perfect order.
In anticipation of moving in, Liza decides to give away her old barbeque, so that she has one less item to move. Julian flies out of Australia on the day Liza is due to move in. When Liza arrives at the house she opens the back door, but the promised barbeque is nowhere to be seen. She texts Julian to ask where it is, but Julian responds "so sorry" and tells Liza that he "had a change of heart" after they signed the contract. He explained that he "started packing up his furniture, then suddenly realized he really needed Betsy in New York". However, Julian hears the disappointment in Liza's voice and says "look, I will ship you a box of Mexican tequila instead". [Note: You should assume the statement regarding the barbeque does not form an express or implied term of the contract, nor a collateral contract]
Can Liza enforce Julian's promise regarding the barbeque by way of equitable estoppel?