We're doing a remodel, enclosing existing front patio to become the foyer of the house. At one side, it's 2" to existing house level, on the other side - it's only 1". What can we use to level it to the existing slab of the house? I'm afraid that the concrete will just break towards the 1" side.

We’re planning to place diamond lath and shoot it on the slab as well.

Any advice?

Thank you.

Enclosing a front patio slab that is uneven is quite a chore. The patio is not a structual member of the house. It contains no foundatin other then the posts that may be on the corners supporting a roof or overhang. You will need to remove this patio. place proper footings around the entire edge to support the new walls and roof. Then re-pour the slab as needed.
Although folks have done this before like you want. They end up having front doors not closing properly, gaps develop under the walls when the slab moves during freeze thaw cycles and a host of other issues. I do not suggest doing it this way.