A colloquial idiom, meaning 'soon' (or 'anon'). Almost always used in referring to oneself, as in "I'll be there in two shakes of a lamb's tail", never used in the imperative "Be here in two shakes of a lamb's tail". Sometimes just abbreviated to "two shakes".
A rather amusing expression, I've always thought. Whoever thought of associating a lamb's tail to time? Some bored shepherd maybe, impatiently waiting for his son to return with drinking water…