How does the Rakshasa know about GWM? And even if he knows and has the Barbarian do it, chances are the Barbarian is not going to be doing 140ish points of damage without raging and with -5 to hit.
Rak: Dominates. One save. (15% out)
Assuming that the Rakshasa does not attack itself for fear of negating the spell, the rest of the spell ends up being:
hit 1 time: 26% out, 23 damage
hit 2 times: 39% out, 46 damage
hit 3 times: 48% out, 69 damage
hit 4 times: 54% out, 92 damage
hit 5 times: 62% out, 115 damage
hit 6 times: 68% out, 138 damage
The odds of him saving before taking 140 points of damage are greater than the odds of him saving after taking 140 points of damage.
And if the Barbarian criticals himself, he takes the damage, but also gets 10 temp hit points. So, a critical with a Sword of Lifestealing drops a few hit points from future hits.
But when the Rakshasa telepathically tells the Barbarian "attack yourself, using your strongest attacks possible", how does the Rakshasa know about raging, and damage resistance, and the sword of life stealing, GWM, etc.? Dominate Person does not give the attacker telepathic clues about the capabilities of the target.
These seems like some metagame knowledge by the DM. Either the Barbarian should be going all out, or just doing normal attacks. The Rakshasa knowing the best combo for the situation should not typically be allowed. Granted, the Rakshasa could ask the Barbarian questions before having the Barbarian attack himself, but I wouldn't have him express the answers in metagame terms. For example, would the Barbarian offer up info on "damage resistance" (or in character terms, "ignore pain when raging") when the Rakshasa asks him what his best attack is?
Why would an ancient creature like a Rakshasa not know about a common ability like barbarian rage? I like to play creatures similar to human culture. Humans talk a lot sharing knowledge about the capabilities of their enemies. If you were in a tribe of ancient hunters or fishers, even the common below intelligence hunter or fisher would be full of knowledge about the dangers of the sea or forest including he creatures in it and how to best fish or hunt them. Is it really difficult for you to believe a Rakshasa can assess humanoid enemies merely by looking at them?