// the second referendum regarding Brexit, could be in place as soon as early June. GAWD!. //
Unlikely. The referendum in 2016 required an act of parliament,
http://www.legislation.gov.uk/ukpga/2015/36/contents/enacted . there’s no provision in that act for a further referendum, so it follows that another act of parliament will be required.
As well as being local election day, May 3rd is the day parliament recesses for a week, with a further recess from 24th May to 4th June.
Being realistic, there is no parliamentary time for such a debate to take place.