Most LS Swaps utilize stock for the vehicle mounts, along with adapter plates that allow these mounts to be bolted to the LS engine mounts. A number of companies make adapter plates, and they can be simple one location plates, multiple location plates, or sliding, adjustable plates.
For most applications you’ll want your engine to sit approximately in the same location as the stock engine, but some applications will warrant moving the engine forward, backward or up or down in the engine compartment. Be sure to select a motor mount & adapter plate setup that meets your needs.
It’s also possible to fabricate your own mounts if you have the tools, materials and skills to do so.