In "Eve's Apology in Defense of Women," what does Amelia Lanyer mean when she says, "If eve did err, it was for knowledge' sake"?

In order to get at what Lanyer is saying, we must first examine the context of the quote. Remember that the Church systematically used the Biblical story of The Fall (Adam and Eve's fall from grace in Genesis) to justify it's classification of women as the weaker sex and the reason for Adam's downfall, while excusing Adam's role entirely. (It's also interesting to note that Lanyer published this poem in the same year that the King James Version of the Bible was published.) 

Lanyer turns this interpretation on its head. She points out that while Eve clearly made a mistake, the man was even more culpable. He was (presumably) stronger than she was (line 3), the ultimate earthly "Lord" (4), created first and most perfect (9-10), and had learned from God himself that if he ate of the fruit, he would surely die (while Eve had this information only through Adam) (11-12). Eve was beguiled by the serpent, but all it took for him was for Eve to offer him an apple (22-3)! Just how strong was he, anyhow? 

Lanyer is using subtle yet powerful satire to expose the silliness of the Church's traditional take on the story, a gutsy thing for a woman at that time to do. They lay all the blame on Eve ("on Patience' back," 17) while letting Adam off the hook.* 

* Note that God didn't let Adam off. The Church essentially did, though, by emphasizing how woman was the reason for man's downfall. 

So: 

If Eve did err, it was for knowledge' sake, 
The fruit being fair persuaded him to fall....

She's already pointed out that Adam was "born" first. He's older and wiser and made perfect by God, presumably. Eve at least had a good reason to eat of the Tree of Knowledge of Good and Evil: she did it to learn, to be wiser. The man, though? He did it because she just handed him the fruit. (Again...how weak and stupid is this man, anyway?)

She points out the ultimate irony in the last two lines:  

Yet Men will boast of Knowledge, which he took 
    From Eve's fair hand, as from a learned Book.

Remember that women were systematically barred from education in Lanyer's time; she was an exception to the rule. They were considered not only the weaker sex, but the dumber one, as well. So here, we have more satire that reinforces the power of the line you asked about: Isn't it funny how men talk about how smart they are (and how dumb women are) when in fact it was Eve who ate first--and she had a reasonable motivation, remember: knowledge--and man ate second (with little or no motivation)?