you are not paying attention and what you asking for is invalid. you need to improve your knowledge about force fields and specifically the details of class 2 force fields. this is prerequisite knowledge for conducting
a standard conforming pdb file has NO topology or force field information. it simply contains coordinates (in rather low resolution) and names of atoms (not force field types) according to some naming conventions defined in the PDB documentation.
even if you have additional force field terms in a class 2 force field, those use THE SAME topology information than a class 1 force field (bonds, angles, dihedrals and impropers) and nothing else. so there is NO DIFFERENCE in the TOPOLOGY between the two types of force fields.
what is different however, is the assignment of force field parameters. and for that, as i had already mentioned, it is crucial to assign the correct force field types to the ATOMS. ONLY THEN can a software determine how many different bond, angle, dihedral, improper types are needed.
if you read through the documentation for the read_data command and the class 2 interaction styles, you will see how those additional terms are mapped to the bond, angle, dihedral and improper topology information.
topotools is able to infer topological angles and dihedrals from the bond topology. but if you let VMD guess the bond topology, there is a high risk, that the built in heuristics in VMD will fail somewhere (after this is meant for visualization, where missing a bond here and there is usually not a big deal with biological systems) leading to bogus topology information. topotools does not even try to do a force field assignment and it will infer bond, angle, and other topological types from the constituent atom types. how this is all related to the individual force field at hand and has to be done during the atom typing step, which has to be done BEFORE loading a geometry into VMD for topotools to produce a correct topology. topotools is designed for people who know what they are doing and will do exactly what it is asked for, but will not pay any attention whether this is meaningful for a specific force field.
in short, your problem is a problem of force field parameter assignment, NOT a problem of topology generation.
tools that are known to be able to exchange data with LAMMPS are listed here: https://lammps.sandia.gov/prepost.html