No "lobster back" in the OED?

[Joel S. Berson]

The OED seems not to have "lobster back" = British soldier, although
it does have just plain "lobster" "3. a. A contemptuous name for: A
British soldier. The name was originally applied to a regiment of
Roundhead cuirassiers from their wearing complete suits of armour
(cf. 1d above). In later times it has been referred to the
characteristic red coat.", from c1643.

Should the OED also include "lobster back"?

Joel

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