Don't think that all Y seats is correct.
The LH site will let me book Business fares on the bmiflights to FRA - and having used these flights on numerous occasions in the last 12 months in Business, it has always been fairly full if not completely so. It would be madness for LH not to offer business class on these flights and would drive high yielding traffic to find other hubs.
"This way the airline is fixed with
up to 162 (all Y) seats and a set cargo limit."