Display (walking) direction/route to a custom markers

Is your feature request related to a problem? Please describe.

I'm working on creating a map which has ability to show current location (already done using LocateControl plugin) and has custom markers. I would like to be able to show (walking) route to custom markers from my current location.

Going through bug reports, I found similar request in #484, but in my case it's definitely not solved as part of #669

Describe the solution you'd like

I would like to be able to use plugins such as:

• Leaflet Routing Machine
• Leaflet.Routing

as pointed on Leaflet Routing plugins list

Describe alternatives you've considered

From my current research alternative would be to use different library/backend with Google Maps, but unfortunately there isn't a lot of information on this either.

Additional context

Functionality I would like to achieve

Implementation
folium is maintained by volunteers. Can you help make a PR if we want to implement this feature?

If the time allows yes.

Review related issues #484 and #669, then investigate the Leaflet Routing Machine and Leaflet.Routing plugins linked in the request. Define how a current location and custom marker should be connected to a walking route, including the integration boundary between folium and Leaflet; the feature is done when users can display that route to a selected custom marker.