I'm afraid that there is a big mistake by Google in showing any kind of cycling infrastructure there :) If you check this road in Google Street View, you see galleries (half open tunnels) and regular tunnels, which protect the road before snow and rocks. It is not possible to build a bicycle path on it and the tunnel is too narrow to fit a bicycle path in it.
And now the question is whether Lech is a town located far enough off the beaten path and there will be little traffic, or whether Lech is such an attractive place, there will be a lot of traffic and we will have angry vacationers on the back :)
I will have three quite sensitive people in my group and I would prefer not to expose them to unnecessary stress.
Thanks :)