The input side isn't a problem - just connect all the devices to the 110 line. AC devices are designed to cope with being arbitrarily arranged on the power bus, because in practice, you never can tell how people will hook them up.
Your problem is the output sides of those supplies. The DC outputs may or may not be isolated from the input side; sometimes one side (usually the negative) may be connected to the input's earth-ground, but sometimes the outputs 'float', not connected in any way to an external node. So, you need to establish a common point ground so that the various DC potentials don't 'float' with respect to one another.
This depends on the type of laptop and power supply, some have additional logic signals, etc.
In all likelihood, your lab power supply is not able to provide enough current to power your laptop. Laptops use a good amount of power, if you have the original power supply it came with, you would see a current rating in mA or A. This is the total amperage the power supply can provide, and my guess is that it is at the least, 2 Amps or more. You may be able to charge the battery with your lab supply though.
There are other possibilities too, but without knowing the laptop model and the specs on your lab power supply, I couldn't say. Your lab supply may very well be able to power the laptop, however when the laptop is first turned on, your power supply may not be able to quickly adapt to the load.
Edit
the power supply is able to provide 3 Amps and the Current measurement
shows that consume doesn't exceed 1.5 Amps
There are a lot of possibilities here, perhaps your lab supply isn't accurate or there were power fluctuations. Maybe your adapter plug was not the correct size, so you had a poor or intermittent connection. The laptop may have had an unrelated issue, that caused this problem, I've seen some that turn off as soon as you plug in external power. Perhaps the battery was bad, problem with the motherboard, or maybe a fan wasn't working. There are just a ton of possibilities.
the laptop is an old lenovo...
"the beep and dead" seemed to be a power security act...
HOW can the laptop distinguish between the its adapter
Usually a beep like that is a bios problem or warning. Also, according to this, it seems that Lenovo has different power supplies and depending on what one is used, it will throttle it's performance. A power supply for a laptop doesn't just have to provide power, sometimes there is some data communication/feed back, perhaps even just a way to verify that the power supply is a real brand name one.
Best Answer
It is part of the safety regulations. When deciding which specifications apply for testing, the product application is taken into account as the way of deciding which spec applies. So if a laptop manufacturer provides an external PSU, they will have it tested to the relevant specs, which includes the product category. There is no guarantee it will be suitable for other applications.
For example, if you drive a motor which has accessable metal parts, and that laptop PSU doesn't give you an earth connection back to the socket, unless you make a seperate connection to earth, there isn't naturally one back for you.