Obviously, you are wrong.

The player doesn't need to be 280 Speed to beat you.

The player would need to be 308 Speed to beat you.

Lyssandra has a 24% Speed Aura.

Lyssandra base speed is 110.

Your Lyssandra will get about 27 extra speed during the battle.

You said your Lyssandra has 280 speed outside of the battle.

This means in your Arena Battle - Your Lyssandra will have 307 Total Speed.

All the Enemy Player needs to do is have a Seeker with 308 Speed to win.

I have seen a person who owns a 333 Speed Seeker.

This is 333 Speed outside the battle (No Aura).

If you was to battle this person, They could use Seekers Defense Aura.

They would still go before you.

They have the faster champion.

It seems to me like you need to Farm Dragon more.

You need to work on getting better Speed Gear.

caldarolad said:

my Lyssandra, with the speed aura she's got around 280 speed.  

You definitely need to farm Dragon more, and maybe work on your FW so you can get better speed glyphs.

Alternatively, maybe you can try using a go-second arena team while you're still working on getting your Lyssandra's speed up.