Hull's 1-0 win at Cardiff, coupled with Leeds' draw, means Dennis Wise's side need a miracle to avoid the drop next weekend.
They trail the Tigers by three points and have a massively inferior goal difference.
And the game ended on an even worse note for the hosts when a huge pitch invasion stopped the match for 30 minutes before referee Michael Jones resumed play for the final 45 seconds.
Six managers have tried - and failed - to stop the terminal rot at Elland Road since Peter Ridsdale and David O'Leary combined to spend more than £100million 'living the dream'.
Terry Venables, Peter Reid, Eddie Gray, Kevin Blackwell and John Carver worked through the initial decline while Dennis Wise, with just ten wins from 33 games, will be remembered as the man in charge during Leeds' lowest ebb.
It had all looked so different when Richard Cresswell had fired Leeds ahead with a 12th minute header following David Healy's shot.
Cresswell bundled in the rebound to spark ecstatic scenes in the 31,000 crowd, but Ipswich pulled their way back into the clash and gradually the nerves began to set in for Leeds.
Francis Jeffers had a goal ruled out for offside, Gary Roberts' volley flashed wide and Lee missed a sitter from Jon Walters' cross.
But Lee made amends in the closing stages to ensure Leeds' six-year collapse finally came to a miserable end.