The Mishna on page 9 of shabbos lists activities that people should not start close to the time of mincha, however, if they start, they may continue. One of the these activities is lunch. The Talmud is concerned on page 10 of drinking during lunch and inebriation lest somone get drunk and forgets to daven mincha. The Talmud says that there is no concern for such drunkeness at lunch because Mincha (unlike Maariv) is fixed and required and therefore somone would not get overly drunk and then fail to fulfill his requirement of prayer.
The SD would like to weigh in. This is the beauty of being a Torah Jew. WE are allowed to partake in this world. We are required to eat, drink, be merry, enjoy ourselves, but we always have an eye on the clock. We are always aware that just around the corner is an obligation which does not allow to indulge beyond our ability to do the full will of hashem. While we are allowed to indulge, we can only do so if it does not inhibit our encroach upon our Avodas Hashem
Therefore, have the three martini lunch provided it does not weaken your ability to do the will of Hashem… Well maybe just two.