Your reputation is far more important

I am slow reacting so it is too difficult for me to tell big, important lies - and keep it not be discovered.

But that is not the point. The point is that you as a person will be far more happier your whole life to be honest than some short term gain by telling a "not well intended" lie. I would rather achieve a higher salary via one more job hop if on-the-job promotion is too difficult. Along your life, your honesty will help you achieve a better life, both in spirit and materially.

I don't know how far you are with the new job negotiation, but do think seriously what if they find out AFTER you have left your current position.