At lunch, England were seven without loss, Adam Lyth two not out and captain Alastair Cook five not out after Australia skipper Michael Clarke had declared his side's second innings on 254 for two.
No side have made more in the fourth innings to win a Test than the West Indies' 418 for seven against Australia at St John's in 2002/03.
However, Sunday morning's play was overshadowed not by records but by the concerning sight of Australia opener Chris Rogers leaving the field with a dizzy spell.
He then received several minutes' on-field treatment before walking off unbeaten on 49, with Australia 114 without loss.
Also Read
A team spokeswoman said the left-handed batsman, who had shown no signs of illness before play started Sunday, was still at Lord's.
The 37-year-old Rogers, who has said he plans to retire after the Ashes, missed Australia's recent 2-0 series win in the Caribbean with concussion after being hit on the head while batting in the nets.
Rogers's fellow left-handed opener David Warner, dropped on nought by Adam Lyth in the gully on Saturday, started today on 60 not out.
Warner was missed again, on 66, when a leaping Joe Root at short extra-cover could only get fingertips to a mistimed pull off Mark Wood.
But with a coveted hundred at Lord's his for the taking, Warner fell on 83 when he drove Moeen Ali to Cook at short extra-cover.