Advice on artist attribution and date sought

Possibly Elizabeth Fanshawe (1609-67/8) (detail) © Valence House Museum
Valence House Museum has submitted the following query:
“The attached portrait has been given to us on loan for identification. A handwritten note on the reverse suggests that it is of Elizabeth Fanshawe, née Cockayne (1609-1667/8) by Sir Peter Lely. In 1629 Elizabeth became the 2nd wife of Viscount Fanshawe. We would like to clarify whether this is Elizabeth Fanshawe, so are looking for suggestions on execution date and artist.
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Comments
Lely-esque but apparently not good enough to be by him. Image quality makes it hard to ascertain condition. It is more likely a studio copy, or at least a period copy, of an original by Lely of the 1650s.