You'll have to know what port(s) are used to access that db.
Eg: for HTTP transfers that port would be TCP/80.
Once you know that, you'll have to configure your gateway box (the one connected to both, LAN and internet) to forward all packets for port xxx to that specific LAN client.
try 'man iptables'
the syntax should be something like
iptables -A prerouting -p tcp --dport 80 -j DNAT 192.168.xxx.xxx
iptables -A FORWARD -p tcp --dport -j ACCEPT
Note: in this way you can only have 1 such db-server. If you need more, you'll have to ask some more IP's with your ISP.