\sqrt{s} tells you what kind of "range" you have in discovering new physics. Even at 8 TeV (both beams at 4 TeV), the reach is increased over the Tevatron by a factor of four. This puts the most likely Higgs mass in reach. More extravagant physics may or may not be out of range until the design energy of 14 TeV is reached.
L tells you how long (as in hours of running) it takes to achieve certain statistical significance in a given result. Rarer results take longer to achieve. The difficulties in achieving this goal are not addressed in the article, but are roughly tangential to those of achieving high energy. From what we heard during the couple weeks of running last year, everything was on track to make their goal possible.
What's notable about the article is that the experimentalists are all fairly happy about the performance. While last year's mishap was worse than what anyone hoped for, nobody was expecting to be at the full energy even by now.
On the other hand, it's interesting that the theorists are so pessimistic about the delays. A lot of them have spent the last 15-20 years coming up with predictions for what the LHC will see. A lot of those predictions will be invalidated when the first LHC results are published.