No:
CDC 2007: https://cdc.gov/flu/pandemic-resources/pdf/community_mitigat... p. 25:
“... the effectiveness of pandemic mitigation strategies will erode rapidly as the cumulative illness rate prior to implementation climbs above 1 percent of the population....”
WHO 2006: http://upmc-biosecurity.org/website/resources/publications/2... argues against lockdowns.
The argument against lockdown as ineffective above 1% spread is based on models, see the references. Whether these are good models or not, that's what CDC policy guidance was.
Western lockdowns with many essential workers spreading the virus, especially nosocomially, are even less justifiable. Wrecking the economy, including health care sector employment and facilities, while leaving people worse off on all other health fronts (deferred checkups and treatments), plus the psychological toll culminating in elevated suicides, is not worth hard-to-measure reduction in spread. Lockdowns actually focus spread into shared housing, notably nursing homes. They also select adversely in the face of mutated variants.
Lockdown policy guidance was not based on cold vs. flu or severity of either. I have no idea why you thought this.