The site is https://ibank.nbg.gr
Using "Save all captured data" I can get LastPass to fill the first box that appears (but no grey icon is shown, I have to do it though the context menu)
After clicking the big yellow button (Labeled "Continue") you get the password field, which hasn't been filled by the first action, meaning you have to click the grey button (which appears now, in the password field) or go though the context menu again.
Basically you have to "call" LastPass 2 times to fill both fields. I know this can be different because LastPass works correctly in other sites that handle login in 2 "stages" (first username, then password). Microsoft and Google do it, for example.