Melia Robinson
A Postmates courier.
Speaking at London tech conference TechCrunch Disrupt, Lehmann says the company plans to roll out in the British capital at some point in the second quarter of 2016, following a launch in Canada in Q1.
The San Francisco company follows a similar model to Uber and other on-demand services, using contractors - rather than employees - to carry out its deliveries. These contractors are free to pick their own hours and do it alongside other jobs, but don't have the same benefits regular employment offers.
Its model is focused on quick, low-cost deliveries - like food, coffee or small items that a customer needs fast. In the US, its partners include fast food company Chipotle, and Starbucks.
In June 2015, Postmates raised $80 million (£53 million) at a valuation of more than $400 million (£265 million). According to its website, it now operates in more than 110 different cities - all currently in the US.
London will join these next year.
Uber - the hottest company in the on-demand economy - is also experimenting with deliveries. But Lehmann played down any potential competition there. "Uber is a great company," he said, "but that space is so huge." (Although when he met Uber CEO Travis Kalanick, Kalanick told he he would "see you in the trenches.")
He cited Grubhub and Seemless as competitors. "Let's get bigger than [them] and maybe we can think about taking on Amazon."
Looking forward, Lehmann suggested Postmates - which is currently doing around 1 million deliveries a month - could one day rival incumbents like FedEx in scale. Our model is "defensible at scale," he said, citing FedEx and UPS. "The more scale yo have, the more you can drive down the costs."