Never a lion in the sense he should have been or he was a lion but you don't think he should have been?
Wasn't one and that was probably fair, despite a long international career.
He was unlucky though in that the Lions squad depends a great deal, especially in oversubscribed positions such as the back row, on which team is strongest in the previous five/six nations and who is given the job as coach.
Foley became an international in 1995 which means he covered the 1997 tour of South Africa which was predominantly English and had the Scot Ian McGeechan as coach. France had won the five nations championship, England were runners up with three wins from four and everyone else had a nightmare, with Ireland pretty awful and bottom of the table, so a Lions call up was never likely.
Four years later, the Lions went to Australia and England were still dominant among the home nations. Remember, this was basically the England team that would go on to win the world cup and Graham Henry made them half the squad. The Irish had actually come second in the six nations thanks to scraping a few wins, but were miles behind in dominance and apart from call-ups for injury and shoo-ins like O'Driscoll, Wood and O'Gara, the Irish didn't really feature beyond the second row.
In 2005, Foley was at the end of his international career anyway, but not one Irishman made it into the eight back rows taken to New Zealand.
If you (perhaps wrongly) think of the three back-row positions as relatively interchangeable, as they tend to do more for Lions tours, he was never that near selection I would have thought, always being overshadowed by at least one of his own countrymen such as Eric Miller, Simon Easterby or David Wallace let alone everyone else.
And also, quite simply, both the Welsh and English were churning out loads of incredibly good 6s, 7s and 8s then (think Quinnell, Charvis and Williams, Hill, Back and Dallaglio) so it was pretty difficult for anyone else to get a look-in.
I think that NOT playing for the Lions is not really that relevant in terms of his career. He was old school (play hard, then play hard) and his love of, loyalty to, leadership of and success with Munster is probably rather more important.