The second one is definitely not of the
Herodian style.
Herodian lamps are all pretty much of the same basic design, with absolutely minimal
ornamentation...if any at all. They were generally used by the
Jewish populace, and since
Jewish law frowned upon depiction of anything that could be considered a "graven image", most were very plain.
I don't have access to my books at the moment, but if no one else posts a more definitive opinion, I'll try to find a
lamp similar to yours in them, tomorrow.