According to nslcd.conf(5)
the $var
syntax in map refers to the LDAP attribute name. Be noted that if you are setting OpenLDAP with the standard NIS schema the LDAP tree doesn't store the name of the user's primary group but rather the gidNumber.
You can either
use standard (NIS schema)
$gidNumber
, ie.map passwd homeDirectory "/otherhome/$gidNumber/$uid"
add
group
attributes for users to store the name of their primary groups. You may have to create your custom schema file to achieve this.