tl;dr: any modification can lead to situations where your car feels worse than before. Lowering springs are particularly prone to these situations.
Can lowering springs make the car's handling worse by lowering the
center of gravity?
Yes, for certain definitions of "worse."
Let's talk through some of the basic things that change when going from stock to lowering springs, working our way through the most obvious suspension components:
- Most obviously, the car will be lower to the ground. If there's a big enough bump or dip, your car's body is going to scrape. In a handling situation, this is not good as that's an undamped input to the system. You may need to correct abruptly as wheels suddenly lose grip.
- Also obviously, you will have less suspension travel. This means that the stock dampers will have less distance to absorb the smaller bumps and dips.
Remember that dampers are effectively friction devices. They only do their job while they're moving. As a result, smaller bumps and dips will have a greater impact on the whole suspension system. At extremes, this is when you see cars bouncing down the road: that isn't good for handling.
- In addition, you are now closer to the bump stops. Those are the little bits of rubber that act as the last resort to keep metal from clashing against metal. They're effectively extremely high rate undamped springs. They can feel like you just broke something when you hit them. They have a similar effect on handling as bouncing the body off the road (i.e., a bad one).
- Given all that, you have sped up the weight transfer that will happen when entering a corner. Is that always good? Depending on the application, sure. However, it also reduces your margin for error. Consider an entrance ramp where you hit patches of ice (or sand or anything that will suddenly reduce friction). If you are already approaching a cornering limit and lose grip, you will need to apply steering input quickly to recover. That steering input will take effect more quickly than before and it is easy to find that you have overcorrected, requiring adjustment the other direction. If you haven't increased your reaction speeds when you sped up the weight transfer, you can find yourself trailing the situation and end up operator-induced-oscillation-ing yourself right off the road.
Note, I'm not getting into suspension binding, bump steer, excessive negative camber and increased tire wear because I don't have the right diagrams handy. Those are also bad.
I have heard the statement that the suspension geometry can be off
with the lowered springs and thus actually making the car handle worse
than the stock suspension and also because the stock strut is being
compressed all the time unlike with the stock springs, is that true
that the handling ?
Replacing the stock springs with lowering springs almost always involves increasing the spring rate (so that the new springs can keep you from scraping the ground all the time). When you change the spring rate, you should also change the dampers (they need to have higher damping rates to cope with the higher spring rates or you'll be boinging down the road).
On a different note, what about Coilovers suspension?
Coilovers are one way to get different springs and dampers as a set (though you can also purchase them separately). A matched set can give you a new (or even adjustable) ride height.
They aren't a cure-all. You should consider your goals carefully before purchasing.
My recommendation is always to spend money on tires (and maybe wheels) if you're seeking to improve your handling.