Mark,
The path /var/lib/mysql/"anything" refers to the database itself.
The way to distinguish between two koha installs (provided that
you want the database to be different for them) is to specify
a different database name for each of them (for instance, koha1
and koha2). You'll also probably want to use a different admin
account for ease of administration (e.g., kohaadmin1, kohaadmin2).
You will also want to keep the koha paths different for those two
installs (e.g., /usr/local/koha1, /usr/local/koha2), as well
as have a seperate koha.conf file for each of them (e.g.,
/usr/local/koha1/etc/koha.conf, /usr/local/koha2/etc/koha.conf).
The fastest way to do this is during the initial installation of
Koha, when it asks you those specific questions, though it would
be possible to set it up later on. Of course, the install is not
really setup to handle multiple installations so you'll still need
to customize some things once you have run both installations.
For instance, afaik Koha will always put the koha.conf file in /etc.
Just copy that file to wherever you want to store it and update your
koha-httpd.conf accordingly.