Lyra block lattice is very scalable compared to most blockchains and can easily compete with the scalability of payment networks such as Visa. However, most real life applications do not require 1.4 M tps (the number that Radix claims). Scalability is important, but there are other aspects of transaction processing that are very important too: time of final confirmation, resources required for a client to generate a new transaction. Lyra clients get instant transaction confirmation, and do not require access to the blockchain data (either local or remote) in order to generate new transactions, which means they can run on micro devices while staying offline most of the time.
Lyra client does not need access to the entire block lattice as every account stores transactions on its own blockchain. It does not even require access to the entire account blockchain as the recent block always contains full information about account balance, which is sufficient for creating a new transaction. This feature enables creating superlight clients that neither require local storage nor depend on a particular server and can be deployed on mobile devices, smart cards, and IoT microdevices.
Lyra design allows zero transaction fees for selected transaction scenarios.
Radix transactions are open to the public view. Lyra is designed to support privacy transactions - see Privacy Transactions on Block Lattice for more info.