The painter and decorator reportedly chose to pop the question on the balcony of their £800-a-night hotel suite in Bali at sunset.
Lily and Sam began dating in July 2009. In August 2010, they announced they were expecting their first child, but Allen suffered a miscarriage in November.
Lily's half-sister Sarah recently said in an interview that Lily is determined to be a mum, and that she and Cooper would begin trying again in 2011. A date for the wedding has not been announced.