Ligier has no incentive to murder an Exalt who Exalts in front of him. I mean, what does that accomplish?
The Exaltation literally will Exalt somebody else – most likely somebody out of his reach and influence – basically immediately. The best he gets out of it is a momentary and passing satisfaction, but even that is not going to be much. Remember that Ligier considers a full circle of experienced Solars to be the kind of challenge worth him drawing his sword and fighting personally rather than just letting his weapon fight for him. He’s not going to get any real pleasure out of snuffing out a freshly Exalted Solar, any more than you would get any pleasure from shooting a fish in a barrel.
Further, Ligier likes to think of himself as the magnanimous and cultured heart of Malfeas. Does he not consent to spare those behind walls and roofs his glory as he knows his lessers can not stand to be with him at all times? Is he not the Prince among Princes, the greatest crafter, the finest dancer, the best lover in all of Malfeas? Of course he is. Just ask him.
No, far better to spare this Solar poppet. Let him see that hell has mercy, that so-called ‘demons’ would treat him fairly when the rulers of his homeland would surely have butchered him on the spot. Offer him the pleasures of his palace and his greatest hospitality. Make no effort to undermine his will, for the Solars are notoriously hard to ensnare in the long term. Instead, plant the seeds of doubt and comfort. Let him forever associate the halls of Ligier’s demense with the moment of his rebirth, with safety and comfort and with frank and useful tutelage in the arts of Essence.
Why murder and attain fleeting and inglorious pleasure, when for the cost of a few kind words and an insignificant expenditure of his massive resources Ligier could gain a powerful ally?