As other user said: Organic Maps uses data from OpenStreetMap, so the best thing is to go there and see how the roads in that town can be mapped better, if bike lanes are present, and if other characteristics of the roads that make them more/less attractive to bicycles are tagged.
I understand this can seem daunting to someone who has never used OpenStreetMap, but I’d encourage you to at least add a note on the “death trap road” to let other, more experienced, users know about the issue and check the tagging of that and other roads.
I’m going to paste here the comment I wrote on another post about this same issue:
Organic Maps and OsmAnd are not adding ads during navigation. Nor “promoted pins”. Nor ads when browsing the map. Nor tracking your every move.
Seriously, give them a try. And remember that, if the maps are lacking information, you are free (and encouraged) to improve them on OpenStreetMap.