Very strange input lag/latency problem - help needed

Does using Constrain Delay Compensation solve your issue ?
This behaviour is typical when using EFX’ses like f.e. the multiband compressor.

look in manual on p. 265 and 228
Cubase features full delay compensation throughout the entire audio path. This means that any delay inherent in the VST plug-ins you use will automatically be compensated for during playback, so that all channels are kept in perfect sync (see “About plug-in delay compensation” on page 228).
However, when you play a VST instrument in realtime or record live audio (with monitoring through Cubase activated), this delay compensation may sometimes result in added latency. To avoid this, you can activate the Constrain Delay Compensation button on the Project window toolbar. This function tries to minimize the latency effects of the delay compensation, while maintaining the sound of the mix as far as possible.

kind regards,
R.