I think what you mean by "standard IP Routing mode," is this configuration:
interface <link to switch>
interface <uplink to router>
switchport mode trunk
interface vlan 1
no ip address
interface vlan <not VLAN 1>
ip address 192.168.0.1 255.255.255.0
If no other vlan is designated as native, VLAN 1 becomes the native VLAN by default. It should still send lldp even if it's shut down.
My guess is that you want to do subinterfaces to restrict traffic from the switch to the router. If you have a bigger goal than just seeing lldp, please post that along with a partial configuration from the router interface and the switch (uplinks, VLANs, anything else useful).