Hi agshubham72
You can travel free of charge on both parts: from Lauterbrunnen to Grütschalp and from Grütschalp to Mürren.
EleonoraS_0-1654259277246.png
Both red lines and black lines mean free travel with a Super Saver Day Pass.
Red is for trains, yellow for busses, black for cable cars/gondolas and blue for boats.
I wish you a nice time in Switzerland.
EleonoraS