The lk<DBNAME> file is associated with the mount lock. There is a bit about this on the Ixora web site in the Q&A page on Files. Anyway, it is not a reliable indication that the database is up. The best way to check is to attempt a connection. This is what the APT script db_check.sh does.

I would like to know in how does Oracle check to see the instance is running. In Oracle 7 there will be a sgadef<SID>.dbf file in $ORACLE_HOME/dbs directory, and some time during abnormal situation a database may shutdown without cleaning up this file. You can remove this file and restart the database. But in Oracle 8i there is no such file created when the database is running and there is a file namely lk<DBNAME> is there. We also used to check for the sgadef.dbf file in the dbstart file during system startup.

Is there any similar file in Oracle 8i where we can check, and what is the function of lk<DBNAME> file?