Leaving a battery charge overnight using a bench power supply can cause damage?
Lead acid batteries are typically charged in a CC (constant current) followed by CV (constant voltage) profile. A typical bench PSU should be able to do this, just make sure you set the the current limit and voltage limit on the PSU to match the parameters specified for your battery. For example if you battery says charge at 0.1C to 6.9V and your battery is 4.5Ah, set the current limit to 450mA = (4.5Ah * 0.1C), and the voltage limit to 6.9V. Your PSU will do the rest for you.