In order to be able to use DEX for getting LYR tokens you need to go to https://app.lyra.live/wallet and create an account, PLEASE BE SURE TO SAVE THE PRIVATE KEY on your disk or another form of storage.
Contact an admin on https://t.me/lyra_live and give them your address to give you some LYR token to be able to create an account on DEX that have a creation cost of 10LYR + 1LYR network fee.
After you receive those tokens go to https://app.lyra.live/dex and push RECEIVE button under Tron or USD Tether ( at the date of writing this article only those two external tokens are supported on DEX ), pushing RECEIVE button will create an account that allow you to send Tron (TRX) or USDT on Tron network to DEX.
After you send Tron (TRX) or USDT on Tron network to DEX wait until they are confirmed pushing REFRESH ALL BALANCES button from time to time.
After the tokens arrived on DEX, you can push arrow up button to move them from DEX to Spot account.
Now you can go to https://app.lyra.live/swap and swap your TRX or USDT for LYR.