As far as I know, there isn't any lease time connected with PPPoE. You have the IP address until you disconnect or are disconnected. If you keep your modem/router turned on, and if your line quality is good enough that there are no accidental disconnections, then you could keep the IP until such time as the needs of equipment maintenance require temporarily disconnecting you.
With DHCP, you're assigned the IP and that IP is considered yours for the duration of the lease.The ISP cannot force you to release the IP (they can deny you access while using the IP, but they can't tell your computer to drop the IP)
With PPPoE, you're connected only as long as both sides agree to stay connected, either side can issue a disconnect at any time, and for any reason. The reason might be an idle timeout or a maximum session length, or it might be dynamic (capacity driven, for example) -- I worked for an ISP that had PPP sessions idle timeouts automatically reduced when less then 15% of our active modems were available to accept a phone call. The result was that during peak hours the idle disconnect was significantly shorter then non-peak hours. This avoided the need for artificially low idle disconnects at 3am, but also reduced the odds of a busy signal during peak hours.
PPPoE is the same ball of wax -- It allows an ISP to more easily oversell service (they can have more customers then IPs) then what is possible with DHCP.
As far as your PC I don't know if 'ipconfig /all' shows DHCP lease time (winipcfg in older Win versions did) from your Linksys, but the Linksys should have some setting for that on its LAN. If your Netopia does not give a clue of DHCP lease time to Linksys, then Linksys logs might.
As previously mentioned, there is no lease time for PPPoE (it is not DHCP which is a different protocol). The only time it gets new IP is when it reconnects for whatever reason it was disconnected (unless interrupted so brief it did not actually do PADT to terminate the connection).