Quite right ubetido a lay of the day is usually going against the favourite but you can still profit from exotic betting.
I think what Lucky Lil is getting at, is value for win bettors.
She classes a lay of the day as a poor value horse which is a lay at the quoted odds. In other words she is not saying it can't win, but saying backing it win only, results in longterm poor value and a loss, as it is far shorter than it's true odds / chances of winning.
For example in harness racing Shakamaker is a lay at $1.40 but one would expect it to still win at those odds. Incidentally it turned out to be a lay as it was unplaced AND poor value!