BLM picked up the media account, believed to be worth £3m, following an eight-way pitch involving Naked, OMD, Vizeum, Manning Gottlieb Media, Carat, Smarter and incumbent PHD's Rocket.
Lastminute.com UK marketing director Vijay Solanki said: "BLM understood our brand and corporate values. It will offer fresh thinking, strong media planning and consumer insight."
BANC's first work for the online brand will be a major campaign in the run-up to Valentine's Day, which breaks later this week. The ads claim to "present the consumer with useful and inventive advice on what to select for your lover depending on the freshness of your relationship".