Sign domain certificate like an intermediate certificate authorities

Hello,

Can I use letsencrypt client to sign my domain certificate like an intermediate certificate authority?
(to sign www.mydomain.com using r3 certificate.)

ISRG Root X1 > R3 > community.letsencrypt.org

No.
Only server authentication and client authentication "roles" are supported.

Let's Encrypt does not offer subsidiary CAs from their chain of trust.

Also, the intermediate certificates used have the pathlen set to 0:

            X509v3 Basic Constraints: critical
                CA:TRUE, pathlen:0

(Source: Chain of Trust - Let's Encrypt)

That means that any certificate signed by R3 or E1 can never be a certificate with "CA:TRUE", so any cert issued by R3 or E1 can not be used to sign other certificates.