IL-sah-beh/IL-sah:-beh or IL-zah-beh/IL-zah:-beh was my first instinct, too. That's what my gut feeling told me - and gut feeling is all I have to offer in this case as I never heard the name pronounced, either.
Then, however, I did some more research on the internet and I found a few (really just a few) modern-day Ilsabes and some of them seem to spell their name Ilsabé (like her
http://de.wikipedia.org/wiki/Medaille_f%C3%BCr_Verdienste_im_k%C3%BCnstlerischen_Volksschaffen_der_Deutschen_Demokratischen_Republik and her
http://de.wikipedia.org/wiki/B%C3%BCrgermedaille_der_Stadt_Braunschweig - the woman who was given a medal in 2007), which makes me wonder if they don't pronounce it IL-sah-BEH/IL-zah-BEH or IL-sah-BAY/IL-zah-BAY along the lines of French names like Dorothée (
Dorothee)...
Briefly speaking: I'm just not sure.
Here is one of the historical Ilsabes (there were a few more...):
http://home.foni.net/~adelsforschung1/meck21.htm
Um, I hope we are allowed to post links here? If not so I apologise.