Hello,
Assuming you fill outside the wall with Leca Lättklinker (weight 4 kN/m³), you can either lay masonry reinforcement every other course or reinforcement steel every third course. The Lecawall is built all the way out to the walls and up to the floor slab. Weber has design guidelines for Leca Block where it states, among other things, how to reinforce/build depending on the wall geometry and different fill materials outside the wall.
Not entirely sure if you would keep the existing wall or not, as well as what you mean by support wall, but I think it looks like below. It's also possible to demolish the existing outer wall and build up the Lecawall there instead. It also works to place prefabricated L-supports outside, or alternatively T-supports. I believe the breaking point from L-support to T-support is at a depth of 2 m.