..."the relationship between ordained and lay"...

I think it more clear to call it distinction or relationship between 'CLERIC" and Lay.

There is nothing other than custom enshrined in Canon Law that would prevent a Bishop from extending his presence to  'lay' person and ordaining 'laity'.

In the beginning, everyone was 'laity' - even bishop or 'elders'-- or Apostles, for that matter -- The division of 'cleric' and 'laity' developed much later.