Archive.org has placed online the two early collections of Edward Lear’s letters:
Letters of Edward Lear to Chichester Fortescue, Lord Carlingford, and Frances Countess Waldegrave. Edited by Lady Strachey. London: T. Fisher Unwin, 1907 (1909 edition).
Later letters of Edward Lear to Chichester Fortescue (Lord Carlingford), Frances, Countess Waldegrave, and others. Edited by Lady Strachey. London: T. Fisher Unwin, 1911.
The books can be downloaded in several formats, the one I prefer is searchable PDF as you get the image of every single page and can still search the text (faster than scanning the book index).