Halliday & Matthiessen (2014: 166):
Note however that the meaning of ‘offer’ is dependent only on the particular goods-&-services referred to: if the meaning required is ‘allow me to’, the same form will be heard as a command with let as second person imperative. Hence an expression such as let me go is ambiguous: either offer, first person imperative (= ‘I offer to go’, with the tag shall I?), or command, second person imperative (= ‘release me’, with the tag won’t you? or will you?). An expression such as let me help you is similarly interpretable either way; but here the effect is a blend, since even the second person imperative ‘allow me to help you’ will still be functioning as an offer.