At most one line of text can be selected this way. To move the beginning of the selection to the left, press shift-tab. Then press tab and the end of the selection will advance by a word.
Enter the beginning of the text you wish to copy and the find feature will select it in your window. To select text without using the mouse, press cmd-f to open the find field. There are several ways to select text to copy to the clipboard: This chapter describes features of iTerm2 that go beyond basic usage and are not generally found in other terminal emulators.