I think your specific ask:

how do we switch the lights to green at the time this vehicle comes near the signal

is way out of scope for this project.

Maybe start by reading this Wikipedia page that describes some of the mechanisms that are typically used.

https://en.wikipedia.org/wiki/Traffic_signal_preemption

Sure, thanks I'll check that out @danpat . On another note , could you also point me to any resource for integrating live traffic/historical data from traffic signals for creating diversions on congested routes. I've seen Valhalla have a blog but couldn't any code samples.

OSRM supports updating speeds on edges as a way to consider traffic data, see the wiki page here:

https://github.com/Project-OSRM/osrm-backend/wiki/Traffic

If you want to route around traffic lights and congestion, you'll need to find your own source of data, and use the mechanism described on the wiki page for importing it.

I will say, it seems pretty unreasonable to consider traffic lights for actual routing - light cycles are very short, and the error margin in most sources of traffic data is quite high. I do not think calculating routes to "hit all the green lights" is feasible with OSRM, nor with most sources of data that most of us have access to. Dynamic traffic light timings additionally make it highly unlikely any routing engine could magically send you the right way if your vehicle doesn't have a pre-emption system on board.

Most sources of traffic data implicitly include stop times due to lights in average travel speeds.