Yes. An L-2 spouse is employment-authorised incident to status, so employment is permitted without a separate application for permission to work.
The spouse's work rights come with the status itself
Hypothetical example: This is one of the clearest practical differences between the L classification and TN. A spouse admitted in L-2 status is employment-authorised by virtue of that status, so the spouse may accept employment without first obtaining a separate authorisation, and many employers will still ask for a document evidencing it. Children admitted as L-2 dependants may attend school but are not employment-authorised, and they cease to qualify as dependants at twenty-one.
For a household leaving a farm township, the spouse's employment freedom often changes the arithmetic completely, because a second income can be earned without depending on a second employer sponsorship. Two practical notes. First, confirm what evidence a prospective employer expects to see before the job offer stage.
Second, the spouse's right to work depends on the principal keeping L-1 status, so a change in the principal's employment affects the whole household at once.