While Monero is one of the best privacy cryptocurrencies, it lacks features required for payment applications running in real world retail and banking environments such as instant transaction confirmations, very high scalability (tps), instantly unlocked sender balances, and more. See vs. Bitcoin, Ethereum, Monero, and all other PoW, singleton blockchains for basic differences between Monero and Lyra.
Unlike Monero, Lyra block lattice carries multiple custom tokens representing various cryptocurrencies, reward points, discount codes, and other user-defined assets. A token representing Monero Lyra.XMR will be also traded in Lyra DEX.
While all Monero transactions require fees, Lyra design allows zero transaction fees for selected transaction scenarios.