Are there any verifiable proof on the historicity of Luke?

Many. Luke has repeatedly demonstrated himself to be a reliable historian of the first rank. His work has also been shown by scholars to fit into the precise time-frame in which it was set.

According to Wikipedia..The traditional view of Lukan authorship is "widely held as the view which most satisfactorily explains all the data."[27] The list of scholars maintaining authorship by Luke the physician is lengthy, and represents scholars from a wide range of theological opinion.[28] But there is no consensus, and the current opinion concerning Lukan authorship has been described as 'about evenly divided'.[29] on who the author was.

The 'verifiable proofs' consist to a large degree on historical details and names of places which Luke demonstrates 100% accuracy on, even where he was previously thought to be in error. This 'accuracy test' indicates that the author of these works was personally acquainted with the places mentioned and the relevant geography and location. This alone cannot prove Luke was the author, but it adds to the case, since Luke, if he was the author would be expected to be accurate in these details.