I feel you I've gone 5 times for 1 solar messenger and 4 i repeat 4 CONSECUTIVE arc scholar. Seriously I'm a decent pvp player not the best and I struggle to get to the lighthouse every week as you can see as I've only aquire 5 weapons I miss out on some because it's so tough. I LOVE this game mode super fun super competitive and a real feat of teamwork when you make it work but when I get the same thing 4 times out of 5 when it's so tough to do I honestly think it needs some serious attention. Bungie if you want to extend playtime don't do stupid things like this to people who play and pay for this game religiously. Maybe have a vendor in the lighthouse where instead of opening the chest you can re roll the burn on your weapon but you don't get to choose what one.

It's bum luck. Been three times, Jewel of Osirus twice.