The stone was recovered during the first two days of trial processing through the bulk sampling plant after recent efficiency and security upgrades and came from the "neck zone" of the mine, which is not part of the current over 1 million carat JORC resource.
It also recovered a 6ct diamond from the same zone during the trial processing.
Once the plant's modifications are signed off, it will start processing three 5,000 tonne bulk samples of kimberlite material from the neck, north and south east zones, aiming to add to the JORC resource and mine life.
Lucapa said the building of a new 150t per hour treatment plant with XRT large diamond recovery technology was continuing on schedule and was expected to reach commercial production during the second half of 2018.
The Kingdom of Lesotho awarded the company the 70% stake in the project at the beginning of last year for US$9 million after an international tender process.
Lucapa last year secured a $15 million finance facility to develop Mothae.
The project's total indicated and inferred resource was estimated to be 38.96 million tonnes at a diamond grade of 2.7 carats per 100 tonnes, containing 1.04Mct of diamonds at an average modelled revenue of $1,063 per carat.
Lucapa's shares were trading steady at A$0.29 (US$0.22) Tuesday.