It's their trademark, that they probably didn't want to protect in many different languages.
It has nothing to do with that, it's branding. Check Google France, Spain, China, Russia...they all have localized versions of "I'm Feeling Lucky" buttons. The Japanese and Koreans are English-crazy, so they kept it in English to look hip.
Google throws off ~$3 billion in profit (!) a quarter (!). I don't think this a lack of interest in protecting their trademarks in many different languages is the reason for it being in English.
Japan is already very familiar with the english word "Lucky" and "I'm Feeling" is probably also not difficult. English words are cool and trendy and very commonly peppered around in Japan.
It doesn't translate well into Japanese.
Surprising that the land of Pachinko doesn't have an equivalent of "I'm Feeling Lucky"