I have a nodemcu that i want to keep dhcp-ing and therefore wanted the authentication going. Now i got it to work, your addition to the header was allmost complete. this is what i got working:

conn:send("GET /json.htm?type=command&param=udevice&idx=501&nvalue=0&svalue=".. t .." HTTP/1.1\r\nHost ...

i had to do:
1 copy the sqlite php files
2 configure the directories and passwords
3 install php/sqllite:
sudo apt-get install php5-sqlite
4 make the directory of the database writable for the apache account (security problem)
5 make the database file writable for the apache account
and working ...