Sept 14 (Reuters) - Australian lithium developer Lake Resources NL said a dispute had arisen with Lilac Solutions Inc over the deadline of the U.S. partner achieving some milestones to get a 25% stake in Kachi lithium project in Argentina, sending its shares down 20%.

Bill Gates-backed Lilac considers it has until Nov. 30 to achieve the necessary milestones to earn up to 25% stake in Kachi project, while Lake believes the milestones must be achieved by Sept. 30, the Australian company said in a statement on Wednesday.

The milestones include Lilac completing at least 1,000 hours of operations of the Lilac Pilot Unit onsite at Kachi and producing a feed totalling at least 2,500 kg of lithium carbonate equivalents from onsite operations, Lake said.

Lake, who signed a deal with privately-held Lilac last September to jointly develop the Kachi project, said it has exercised its rights to have the dispute resolved either by agreement of both Lake and Lilac, or by arbitration.

Lake said it has an option to exercise certain buyback rights under the deal if Lilac does not achieve the milestone by the required date.

Recently, short seller J Capital Research had claimed that Lake's plan to produce lithium in Argentina was based on Lilac's extraction process that likely does not work, allegations that Lake has refuted.

Lilac did not immediately respond to a Reuters request for comment.

(Reporting by Himanshi Akhand in Bengaluru; Editing by Rashmi Aich)