Welcome to the forum!
You can run both LionChief and LionChief Plus trains on the same layout, as both systems rely on a constant 18 volts on the track to operate.

As you have seen, running conventional powered trains along with LionChief/Plus on the same track does not work properly.
With LionChief/Plus and also Legacy/TMCC systems, a constant 18 volts is used to power the trains, and speed is regulated electronically inside the locomotive.

Conventionally operated trains vary the track voltage to regulate speed.
When operating conventional and any remote system together on the same track, regulating transformer voltage for conventional locomotives affects the electronics in the remote engines, because they are fighting a varying track voltage when they expect a fixed voltage.

Larry

The different engines in the Thomas series all run on different frequencies, so a Thomas can be run with a Percy for instance.
All the same engines run on the same frequency, so you cannot run 2 Thomas engines or 2 Percy engines at the same time.

Enjoy your trains!

Larry