Giner and Lefeber had two holes remaining in their rounds when thick mist and rain forced a stop to play. The seven leading groups will return to the course early Sunday.
Paul Dwyer from England and Ireland's Philipp Walton had one hole to play and stood at 7-under. Walton was 6-under Saturday but refused to play the 18th.
'I wouldn't play the last. No way,' Walton said. 'Today I putted well and I'm only one back. I've had three bad years and I would love to get back on tour full-time.'
Walton holed the winning putt for the European team in the 1995 Ryder Cup at Oak Hill but currently depends on rare invitations to play on tour. He does not play the Challenge Tour.
England's Andrew Oldcorn and Italy's Massimo Florioli were also at 7-under. Florioli had completed 51 holes and Oldcorn 50.
Ilya Goroneskoul and Des Terblanche are tied for the clubhouse lead at 4-under 212. Andrew Sherborne, who shot a 6-under 66 Saturday, is tied for third at 213 with Mathew Blackey.
Steve Webster from England shot 70 to finish at 214 and Benn Barham also from England finished a further shot back at 215 after a 71.
Full-field scores from the Madeira Island Open