We can consider three things that could exist (but I believe one of them is not presently available):

Certificates for an RSA public key you picked, signed by Let's Encrypt R3

Certificates for an ECDSA public key you picked, signed by Let's Encrypt R3

Certificates for an ECDSA public key you picked, signed by Let's Encrypt E1
With (1) your servers will do RSA signatures to prove their identity (or, with obsolete clients, use RSA to decrypt secrets chosen by the client). Let's Encrypt used RSA to sign the certificate. The client will use RSA to verify signatures from your server, and the signature on the certificate itself.
Under (2) your servers make ECDSA signatures to prove their identity (obsolete clients which expect to send encrypted key material are not supported). Let's Encrypt used RSA to sign the certificate. The client will use ECDSA to verify signatures from your server, but RSA to verify the signature on the certificate.
In future with (3) the signature on the certificate will be ECDSA too, but this changes nothing about what happens on your servers, it only potentially reduces work for clients (visitors to a web site for example) because now they're doing ECDSA verification which (depending on hardware) may be easier.