The Dictionary of the Anonymous and Pseudonymous Literature (1882-88) was compiled by two Scottish librarians, Samuel Halkett and John Lang. Their entry for Lives of Scottish Poets is sourced to the Advocates' Library in Edinburgh, where Halkett had been keeper from 1848. The attribution to Joseph Robertson has been widely adopted by cataloguers, though it seems worthless since no particular Joseph Robertson is specified.

My best guess is that the intended reference is to Joseph Clinton Robertson (1788-1852), the Sholto Percy of the Percy Anecdotes (1821-23) published, like the Lives, by the firm of T. Boys. Robertson, though a London journalist, was born in Scotland and may well have been involved with the project.

Samuel Halkett, John Laing.
A Dictionary of the Anonymous and Pseudonymous Literature of Great Britain.
Edinburgh: 1883.
Vol. II. pp. 1501-02.