The problem is: some laptops battery can't be removed. If I just keep
my notebook charging while I use it, will the battery still lose
lifecycles? Is there another way I can prevent battery from losing it
I have a Lenovo X230 beside me here that is always ON, charging to 80% max (and never drops below 70%). The cycle count was 450 cycles some months back and remains at 450 cycles. So cycle count largely does not increase while always plugged in. Starting from 80% shows remaining time of 2 hours unplugged. This is a 7 year old machine, second battery and design point was 3 - 4 hours when new.
On my production X1, I charge the battery to near full, use it, allow to discharge (not fully), charge, repeat. The cycle count has increased from under 350 a while back to over 400 now. So using the battery normally increases the cycle count. This battery is the second one (replace by my local shop) and is still good for about 5 hours or so of use before I need to charge it. Design point is 6 hours.
To your last question, other that the above, batteries will always wear out. No way to prevent that. Laptop batteries are mean to be used and not just left plugged in forever but you can do this without a lot of damage.