Q.would lyches roots be dangerous if planted close to the house?
none

Lychee is not a large growing tree, but it will do best if given enough space to put out an extensive absorbing root system.
The roots are not likely to damage a substantial concrete house foundation, and it won't grow large enough to over hang the house with hazardous limbs or top. But I would recommend planting it at least 8 to 10 feet away from the house wall so that you don't have to worry about roots, or branches rubbing hard against the wall and having to prune it back hard.