Is there one word for last week, in a similar way that two weeks is a fortnight?
Surprisingly, it would appear that there is such a word:
yesterweek n. 1. The week last past; last week. - Webster's 1913 Dictionary
yesterweek noun 1. last week. adverb 2. during last week. First recorded in 1830-40; yester- + week - Dictionary.com
Ngram suggests that the word has had some currency in the language:
Here are a couple of examples of its usage (emphasis, mine):
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I did not have the mother's milk necessary for an ointment for the eyes. so I used garlic and goose far left from Cloctoring Morwenna's boils yesterweek. - "Catherine, Called Birdy" By Karen Cushman
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"TDearly beloved brethren : Bruno and Nolan ; bogholders and stationary lifepartners off orangey Saint Nessau Street were explaining it avicendas all round each other ere yesterweek out of Ibn Sen and Ipanzussch. - Finnegans Wake by James Joyce (book III, chapters 1-4)