As @serverco said, you should always use the fullchain generated when issued the cert and you won't have this problem.
Just for your info, you have issued the cert today so you are using the wrong intermediate cert, it is not X1 but X3, since last week there is a new intermediate cert in play ;-).
X1, X2, X3, X4 are just versioning numbers. Certificates were issued by X1 at first, X2 would have been a recovery intermediate if something goes completely wrong. X3 and X4 are the new intermediate certificates that work with Windows XP SP3+. Your client should automatically download the right certificate from Let’s Encrypt, if it does not, you should report it as bug there. It’s never a good idea to hardcode the intermediate.
Anyway, you don’t need to issue a new certificate with the updated script (yes, update the script to the new version) but you only need to concatenate your current cert and the new intermediate cert https://letsencrypt.org/certs/lets-encrypt-x3-cross-signed.pem into lisitede.chained.crt