The idea that bike riders would not pay tolls sufficient to cover the costs of operating bike lanes totally ignores what bike riders do pay for, how they pay for it, and the fact that not just the bike riders benefit from the existence of the infrastructure for instance. If the intent was a thorough economic analysis it would include a lot more variables as well. Finally, sour grapes is a good word for it - traffic in London is a mess with or without bike lanes with TfL having multiple concurrent programs that should be included in the discussion including the Congestion Charge scheme.
Basically, the article was a drive by, not a serious analysis piece.