Orgasm is not the goal of the Lingam massage although it can be a pleasant and welcome side effect. 
The goal is to massage the Lingam, also including testicles, perineum and Sacred Spot (prostate) 

externally, allowing the man to surrender to a form of pleasure he may not be accustomed to. 

From this perspective both receiver and giver relax into the massage.

Men need to learn to relax and receive. Traditional sexual conditioning has the man in a doing 

and goal oriented mode. The Lingam Massage allows the man to experience his softer, more

 receptive side and experience pleasure from a non-traditional perspective.

Beginning the Lingam Massage   Have the receiver lie on his back with pillows under his head so he can look up at his partner(giver) Place a pillow, covered with a towel, under his hips. His legs are to be spread apart with the knees  slightly bent (pillows or cushions under the knees will also help) and his genitals clearly exposed for the massage. Before contacting the body, begin with deep, relaxed breathing. Gently massage the legs, abdomen, thighs, chest, nipples, etc., to get the receiver to relax. Remind the receiver to breathe deeply and to sink deeper into relaxation.Pour a small quantity of oil on the shaft of the Lingam and testicles. Begin gently massaging thetesticles, taking care to not cause pain in this  sensitive area.Massage the scrotum gently, causing it to relax.Massage the area above the Lingam, on the pubic bone.Massage the perineum, the area between the testicles and anus.Take time  when massagingthe shaft of the Lingam.Vary the speed and pressure. Gently squeeze the Lingam  at the base with your right hand, pull up and slide off, then alternate with your left hand. Take your  time doing this,right, left, right, left, etc. Then, change the direction by starting the squeeze at  the head of the Lingam and then sliding down and off. Again, alternate with right and left hands. Massage the head of the Lingam as if you are using an orange juicer. Massage all around the head  and shaft. In Tantra there are many nerve endings on the Lingam that correspond to other parts of the body. It is believed that many ailments may be cured by a good Lingam massage. The Lingam may or may not go soft as you perform this technique. Do not worry if it doesn't get hard again. You will probably find that it will get hard, then go soft, get hard again, etc., which is a highly desirable Tantric experience, like riding a wave, bobbing up and down. Hardness and  softness are two ends of the pleasure spectrum.   If it appears that the receiver is going to shot out , back off, allowing the Lingam to soften a little before resuming the massage. Do this several times, coming close to shot out, and then backing off. It is important to remember that the goal is not orgasm in and of itself. Men can learn the art of ejaculatory mastery and control by coming close to shot out and then backing off on the stimulation. Deep breathing is key here and will soften the urge to shot out . Eventually ejaculatory mastery will allow you to make love as long as you want and you can become multi-orgasmic without losing a drop of semen. Orgasm and shot out are two different responses that you can learn to separate. The result is a very expanded sex life.   The Sacred Spot Find and massage the male Sacred Spot. There is a small indentation about the size of a pea or  maybe larger midway between the testicles and anus. Be gentle and push inward. He will feel  the pressure deep inside and it may be uncomfortable at first. Eventually, as this area is worked  on and softened, he will be able to expand his orgasms and master ejaculatory control. You can  massage his Lingam with your right hand and massage his Sacred Spot with your left hand. Try pushing in on this spot when he nears shot out. The man may have strong emotions come  up during access to the Sacred Spot. Be the best friend and healer he could have in that moment.  You, the giver, are creating a place of trust and intimacy.