It is a cross over between the series Lupin III and Detective Conan and takes place after the television special Lupin the 3rd vs Detective Conan. The plot follows Conan Edogawa who sets out to apprehend Arsène Lupin III, the suspect of stealing a jewel called Cherry Sapphire.

(Souce: Wikipedia)

A dying mob boss entrusts Lupin with a diamond that supposedly is the key to a vast treasure. But when Lupin is attacked by an assassin and saves a mysterious girl from trouble, it becomes clear that that there's more to this treasure then meets the eye... 

(Source: ANN)

Lupin & co. attempt to steal two face plates from millionare Michael Sizuki, thinking that they will lead to an ancient treasure when brought together. However, it soon becomes apparent that there is more behind the plates then meets the eye. 

(Source: ANN)

In a country called Vesparand, a new mineral with super stealth properties has been discovered which attracts Lupin's attention. At the same time the untimely deaths of Queen Sakura and her son, Prince Gill, leave Princess Mira next in succession to the throne. During a trip to Japan, Princess Mira finds her double in Ran and takes the opportunity to trade places, which ends with Ran being spirited away to Vesparand with Conan, Zenigata, Kogoro Mouri, Lupin and Fujiko in tow. There they meet a waiting Jigen and solve the mystery of the deaths of the Queen and Prince. (Source: ANN)