The agency won the business following a pitch against Underwired, and will now work on a series of digital communications that help the island, which is located off the west coast of Ireland, launch a range of businesses and products.
These include food, toiletries, health supplements and jewellery products, all sourced from the island.
The pitch for the account was called in March and was handled by Oystercatchers.
LMFM's first campaign will launch later this year and will include digital creative, social media and web design work.
Inishturkbeg Ventures was set up by chief islander Nadim Sadek, the former worldwide commercial and strategy director for the WPP-owned data company Research International.
The branded goods already being sold by the island include a line of smoked fish products that is currently stocked by Harrods and is soon to be available from Waitrose.