Why are 3 equivalents of organolithium needed in synthesis of ketone from carboxylic acid?
The text box you are quoting from (p 219) refers to this specific reaction. The compound in question possesses an α-hydroxyl group, which needs to be deprotonated too.

Notice that three equivalents of organolithium are needed in this reaction: one to deprotonate the acid, one to deprotonate the hydroxyl group, and one to react with the lithium carboxylate. These chemists added a further 0.5 for good measure.



However, the scheme directly above this incorrectly indicates that 3 equivalents of MeLi are required for a generic carboxylic acid:

In the absence of any other acidic groups, only 2 equivalents of organolithium are needed. In practice, however, more than 2 may be added.
Note that the 3 protons are still needed to get to the protonated species shown directly afterwards. In practice the proton source (e.g. saturated aqueous $\ce{NH4Cl}$, or just plain water) is usually added in excess.