A series of citrate salts were tested as hydrogen bond acceptors to synthesize deep eutectic solvents (DES) based on lactic acid and glycerol, used as hydrogen bond donors. The DES produced were then screened to identify the highest performing system for the effective extraction of polyphenolic phytochemicals from the medicinal plant Salvia fruticosa Mill. (Greek sage). The most efficacious DES was the one composed of lactic acid and sodium citrate dibasic, at a molar ratio of 15:1 (LA-SCDB15). Furthermore, for the first time there has been evidence concerning DES pH and extraction efficiency. Using this solvent, a batch, stirred-tank extraction process was developed, by employing ultrasonication pretreatment and response surface methodology. The optimal settings determined were stirring speed 900 rpm, proportion of DES/water 77% (w/v), and ultrasonication pretreatment time 15 min. By adjusting these optimal settings, the predicted maximum total polyphenol yield was calculated to be 79.93 ± 1.92 mg gallic acid equivalents g−1 dry mass. The examination of temperature effects demonstrated that the batch, stirred-tank extraction stage was very energy-efficient, with a barrier of 7.64 kJ mol−1. Comparison of the extraction of Salvia fruticosa polyphenols with other green processes previously developed, illustrated the high extraction capacity of LA-SCDB15. The major polyphenols identified in the extracts produced under optimized settings were chlorogenic acid, luteolin 7-O-glucuronide and rosmarinic acid.