In most ways, what CA you're using doesn't affect performance. If it does affect performance, Let's Encrypt is probably one of the faster CAs.
When you're running the same algorithms to verify cryptographic signatures, it doesn't really matter what the names involved are.
Some of the choices a CA makes can affect performance -- for example, if they use larger and slower 4096-bit RSA intermediate or root certificates. Let's Encrypt doesn't.
For the limited number of clients that use OCSP to check whether certificates are revoked, if the CA's OCSP servers are slow, that would make connecting slower. Let's Encrypt should have one of the faster OCSP setups. But most clients don't check OCSP, and some servers can avoid the issue if they have a good OCSP stapling implementation.
In any case, I'm just being pedantic. It doesn't matter. You'll almost certainly never notice a "performance" difference between different CAs.