You can run LMCE with a single NIC, as explained in the wiki's DHCP entry section on "Single NIC".
What this setup requires is that LMCE run as the only DHCP server on the network, which means that if your switch, or any other device on your network, is assigning IP#s by running a DHCP server, then that old server has to be switched off. There probably is one running, or else how would your notebook have gotten its old IP#? If it got it by manual assignment, then you have to either continue manually assigning an IP# on the subnet that the LMCE DHCP server is on and assigning in, or you have to set the notebook to get its IP# by DHCP. Which is a first step to getting the notebook to boot by PXEboot anyway.
Then you have to make sure any other machine connecting to the LMCE server is also set to get its IP# by DHCP, or is manually set to a number on the LMCE subnet. You make them all on the same subnet by looking at the IP# that LMCE is assigning itself (in its Network Settings, but default is 192.168.80.1) and manually assigning numbers in that subnet to the other machine, or setting the LMCE DHCP server to assign IP#s on the other machines' subnet (and excluding those other machines IP#s from the range assignable by LMCE, to avoid conflicts) or by setting the other machines to use DHCP, which lets LMCE assign their IP#. Pick the method for each machine, including LMCE, that lets them all share the same subnet. Often routers/gateways (like cablemodems etc) don't allow using a DHCP client to set their internal LAN IP#, but either assign themselves one from their own internal DHCP server, or let you set them manually. Since that internal DHCP server must be turned off, you'd have to set it manually.
There are more details on working around bugs in LMCE DHCP configuration included in that DHCP wiki page.
Please return the favor of all this help by letting us know how it goes for you. If it still doesn't work, and this is a new case, we can fix it and document the scenario for the next person to encounter it.