Flannery, the Ireland hooker, suffered an elbow injury in training that requires surgery and has ruled him out of the tour to South Africa.
Wales winger Halfpenny remains part of the squad but requires intensive treatment on a thigh injury and will not travel to Johannesburg with the squad on Sunday evening.
Halfpenny is expected to be sidelined for around a fortnight and he will join the squad in South Africa if his recovery goes to plan.
But with the Lions facing such a short build-up to the first Test and Halfpenny likely to be unavailable for the first two matches, McGeechan has decided to call up a replacement back.
England full-back Delon Armitage is considered favourite not only because he can cover the back three and outside centre but because he offers the Lions a goal-kicking option.
The Lions are only travelling with two front-line kickers in fly-halves Stephen Jones and Ronan O’Gara, with Riki Flutey and Halfpenny to provide back-up.
With goal-kicking a prerequisite, other potential candidates could include Wales’ James Hook, Scotland’s Chris Paterson or England reject Danny Cipriani.
Former Ireland and Lions hooker Keith Wood has backed Ulster’s Rory Best to replace Flannery, although Scotland’s Ross Ford is also on the official standby list.
The Lions squad – minus those players from Northampton, Leicester and Leinster, who have European finals this weekend – spent the day sailing on the Solent in a bid to accelerate team bonding.
The Lions’ first tour match is against a Royal XV in Rustenburg on May 30.
Meanwhile Shannon RFC insisted last night Alan Quinlan and Jerry Flannery will always be considered Lions to their club.
New club president Martin Clancy said: “The initial recognition of both players’ on the Lions touring side was a supreme and deserved honour we shared with them as Shannon men.
“Despite not having the opportunity to don the famous red jersey, we will always consider them as Lions.”