Hallo ginnyTheCat,

for the cycle lane between the two car lanes (1) I wouldn't add cycleway=no, but cycleway:left=no + cycleway:right=lane + cycleway:right:lane=exclusive.

The road section still has a cycle lane in the westwards direction. The lane is just not located on the very very right of the street.

Best regards
map per

(1)  https://www.openstreetmap.org/way/58561799