I'm assuming so, but apparently you're allowed to loot the chest every weekly reset, which leads me to believe that if you've gone flawless like myself and many others, that each week you are entitled to another randomly generated set of top-tier gear and rewards.
If this is the case then wow, that is awesome! The chest is on a weekly reset according to PlanetDestiny.
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The Lighthouse isn't permanent. You have to go 9-0 on ToO to reach it everytime.