>>1413809This is why you have things like a general plan or active transportation plan. These documents help to guide development and infrastructure projects. So it is unlikely you would have a major conflict like this. That being said the cost of a cycle track compared to the cost of light rail is like a drop in the ocean. Developing light rail would certainly take priority over all bike infrastructure.
Also to get those grants, you need to have very detailed plans on the alignment of the rail lines, ROW acquisitions if needed, who it will serve, and how it will function in the greater transportation network. By the time a city gets a grant they would need to already have plans on how the bikeways would be built, removed, or modified to work with light rail.
The more interesting question is if you are designing a bike network with consideration to existing and future bike counts, land use, collisions. etc... do you plan and build bikeways along corridors where there is already an existing demand or do you try to develop new corridors based on "if you build it they will come" strategies? Do you risk spending money and resources on planning, designing, and building bikeways that may never get used?