Is it possible to transfer my domain name registration from another registrar to LAMP Host and renew it through LAMP Host instead?

Yes. You will however need to initiate a registrar transfer of your domain name in order to renew it through LAMP Host. By transferring your domain name to LAMP Host you are automatically renewing it for 1-year as well.

For example, if your domain name currently has 45 days to expiration, transferring it to LAMP Host will add 1 year to your current expiration date and leave you with 1 year and 45 days until expiration.