Referendum solves nothing.
If it is a re-run of previous ref (binary leave/remain) then it is an affront to democracy.
If a ref is held at all then it should be deal/no deal
If a ref is held and Remain is in the ballot paper, then there must also be options for deal & no deal. 'Leave' should be counted as the total of both leave options and if leave wins then the highest of deal/no deal wins over all.
If Remain wins on less than 51.89%, or on a turnout of less than 72.21% then the result is invalid as it will not have overturned the previous result.
None of it matters though, because if leave wins again, then the Lib Dems & other remainers have already stated that they will not accept the result.
Ergo, nothing at all is solved by having another referendum.
The only way to break the deadlock is a GE, with all parties standing on honest Brexit positions.