What the Constitution says ...
Illinois Constitution
Article V -- The Executive
Section 4. Joint Election
In the general election for Governor and Lieutenant Governor, one vote shall be cast jointly for the candidates nominated by the same political party or petition. The General Assembly may provide by law for the joint nomination of candidates for Governor and Lieutenant Governor.
Instant Analysis: Appears to spell out that yes, lawmakers can change how the lieutenant governor and governor are paired without having to change the constitution. They run separately in the primary but as a ticket in the general. The constitution says lawmakers can pass laws that create a ticket for the primary.
But of course we're not past the primary. Can they pass a law taking an election win away?
We can't undo Cohen and Plummer, 27. We can prevent more Fairchilds and Cohens.