LKO PPTA has an ICE currently but due to the heavy distance, it has bad timings. A VB express might correct this, assuming it can get the passengers required. Lucknow - Patna via Varanasi will need to go via Sultanpur and it'll terminate at proper PNBE if it goes via there.
Bhopal Lucknow can be done, but I am skeptical about the distance there and how much mps the tracks will require. It's not about the mps of the trains in most cases, it's of the tracks. If the tracks are...
more... improved[and CNB LJN is in bad condition], even normal trains can get a boost in speed.