You can specify more than one interface in your lxc configuration file. Just add the interfaces one after the other and use lxc-create to create your container, like this:
lxc.network.mtu = 1500
lxc.network.type = veth
lxc.network.name = eth0
lxc.network.link = br0
lxc.network.ipv4 = 107.20.135.109
lxc.network.flags = up
lxc.network.type = veth
lxc.network.link = br1
lxc.network.ipv4 = 192.168.0.63/24
lxc.network.name = eth1
lxc.network.flags = up
Inside your container, if you do an ifconfig, you should see two network interfaces.
This was not documented very well and I found this after a bit of frustrated googling.