Painted Wall Demolition
"would demolition of painted wall be done in a special way so that paint dust (with lead) does not spread?"


YES, if a professional contractor is performing the work they will have the materials checked for the presence of lead and either take appropriate measures to protect their workers and the public (if they have the expertise, equipment, and license required), or subcontract with a specialty outfit for lead abatement.

NO, if this is a substandard, unscrupulous, or ignorant contractor; or if there is no regulatory driver for such considerations in your part of the world.