Just checked the docs for installation and found out that the script included in the page only has repos for 7 to 10:
This certainly is not a surprise considering the Bullseye has been released only a couple of days ago 
I was waiting for Debian 11 release to set up a new server and would really like to give the OpenLiteSpeed a chance on it. Does anyone knows how long does it usually take for a new repo to appear for new OS releases?
Bash:
if [ $ID == "debian" ]; then
echo "detected OS: $ID - $VERSION_ID"
echo " now enable the LiteSpeed Debian Repo "
if [ $VERSION_ID == "10" ]; then
echo "deb http://rpms.litespeedtech.com/debian/ buster main" > /etc/apt/sources.list.d/lst_debian_repo.list
echo "#deb http://rpms.litespeedtech.com/edge/debian/ buster main" >> /etc/apt/sources.list.d/lst_debian_repo.list
elif [ $VERSION_ID == "9" ]; then
echo "deb http://rpms.litespeedtech.com/debian/ stretch main" > /etc/apt/sources.list.d/lst_debian_repo.list
echo "#deb http://rpms.litespeedtech.com/edge/debian/ stretch main" >> /etc/apt/sources.list.d/lst_debian_repo.list
elif [ $VERSION_ID == "8" ]; then
echo "deb http://rpms.litespeedtech.com/debian/ jessie main" > /etc/apt/sources.list.d/lst_debian_repo.list
echo "#deb http://rpms.litespeedtech.com/edge/debian/ jessie main" >> /etc/apt/sources.list.d/lst_debian_repo.list
elif [ $VERSION_ID == "7" ]; then
echo "deb http://rpms.litespeedtech.com/debian/ wheezy main" > /etc/apt/sources.list.d/lst_debian_repo.list
echo "#deb http://rpms.litespeedtech.com/edge/debian/ wheezy main" >> /etc/apt/sources.list.d/lst_debian_repo.list
fi
