Would Lowering my Handlebars Help my Performance?
If you are looking for pedalling performance, adjusting the seatpost (up and down) and the seat (back and front) is the answer. There are literature about adjusting seatpost so you can look them up on the internet; youtube also have many video demonstration.

Adjusting handlebar height is more about efficiency. In general:


the less up-right position, the better the efficiency. This helps a lot when you are riding at high speed (noticeably at speed 20 mph+ or 35 kmph+), or against the wind. However, there is always a compensation for riding aggressively: you tire out quickly
the smaller the handle bar, the better the efficiency. The best efficiency is when the arms are shoulder length apart, just similar to the riding position on aero bar.
arms at some angle also lower your riding position and improves efficiency.


Your bike looks like a hybrid, which gives out that you mostly ride in urban area. Adjusting handlebar height is thus beneficial because you are likely to hit 20 mph+.