Grossglockner from Lienz, please

On my way back from the Dolomites (train + bicycle), I'm thinking to climb the Grossglockner in Austria. The "normal" route seems to be the one from Fusch. I'm thinking of doing actually both: Fusch -> Grossglockner -> Lienz -> Grossglockner -> Fusch.

No much info online on the segment Lienz -> Grossglockner -> Fusch.
Can anyone share info on it?
Thanks,

Alberto