best weapon for Oscar at TT

I think Oscar os ok with saphire lance+ maybe you shall give him am bluetome breaker or lance breaker that will give you advantage against blue and red units whichone are the most

The logic behind running TA and "Gem weapons" is that you're already at a disadvantage against your opposing colour, so it's not like making it a lot worse makes a significant difference if you keep it in your control. My Azura always did just fine countering Reds with it, and I kept her away from Greens as much as I could.

Oscar is the best Cavalier at running Firesweep, so you could go for that if given the chance. You also happen to get one of the best IVs, which is +Atk. A good idea would be L&D (since it's not like he's taking many hits as it is) and Desperation. For specials, I'd go for one of Moonbow or Luna/Dragonic Aura if you don't mind the extra cooldown.

If you're on a budget, Sapphire Lance+ & Lancebreaker 3 should be good enough for TT? Slays all reds + lance units. Since none are optimal, not worth killing a 5* unit for their Silver/Killer Lance+, instead best to save the human sacrifice for when you actually get a weapon more close to his optimal, like Firesweep+ or maybe Brave Lance+ imo.

His native lance is ok on him. It gives him a lot of coverage. But if you're going to use him for TT, you will probably want either a healer to support him and keep him in lancebreaker range, or just run a different kit with him. He's a great Brave Lance quad unit. He's also a little better than Roderick with the Firesweep Lance. Killer Lance+ with Moonbow and Renewal isn't a terrible option, but it's kind of niche, and might not be enough for TT. Silver Lance+ isn't worth it on him. I'd say if you're set on using him for TT, use his base kit + L&D or Fury and Moonbow/Luna/Draconic Aura. And you'll want a healer to support him. You'll want a really solid red unit to cover his weakness to greens for TT. Maybe a Ryoma, Xander, Eldigan, or pretty soon the Black Knight himself. That leaves room for a healer and one more slot, maybe a Brave Bow user or a green to counter stronger blues than Oscar can comfortably face.

Honestly, it depends whether you have the fodder for him and your plans for this TT. Go for Killer Lance if you don't like Gem weapons, Silver at least. If you're auto-battling, then swap his weapon ASAP since the AI is awful if you have good Arena experience. This is, of course, assuming little goes in him. I rolled Gray while rolling for Celica. Taught him his skills for the two weeks, and he's now my SP-grinding catalyst for swords. It's very possible to do the same for Oscar, especially since he gains +10HP and +4DEF/RES for being a bonus unit.

TL;DR: Keep Sapphire Lance, swap it instantly if auto-battling.

I would probably just stick with Sapphire Lance and Lancebreaker for TT. That should be enough for all reds and most blues. I just don't think Oscar's good enough to sink 40k into him for L&D 3 and Firesweep Lance.