Edit: Uwe posted his answer 8 seconds before mine. I've run his numbers using moles, and come to the same conclusion.
There is 1.0 lb O$_2$ x (1000 g / 2.2 lb) x (mol O$_2$ / 32.0 g O$_2$) = 14.2 mol O$_2$ available.
The cartridge contains 2.7 lb LiOH x (1000 g / 2.2 lb) x (mol LiOH / 23.95 g LiOH) = 51.2 mol LiOH.
2 moles of LiOH scrub 1 mole of CO$_2$. This means 25.6 mol CO$_2$ can be scrubbed.
Since 6 mol O$_2$ are metabolized to 6 mol CO$_2$ -- a 1:1 ratio -- this means that the O$_2$ will run out before the CO$_2$.
It depends. All of the suits leaked to some degree, even though they weren't supposed to. The only suit that leaked badly enough to be considered a failure was Apollo 12 commander Charles Conrad's. Leaks caused oxygen to be drawn from the supply at a faster rate, to maintain suit pressure.
However, in most cases, the CO$_2$ scrubber will indeed fail before the oxygen supply runs out. A 1% increase in CO$_2$ concentration is deadly; a 1% decrease in O$_2$ is not.
It's also possible for the cooling water to run out first and the astronauts to overheat, depending on physical activity level and solar exposure.