You can connect a display with different specifications but you don't want to mirror the displays. You would want to change to only output to the external. That will allow you to set a mode that wouldn't work for the internal display but will work for your external.
You actually can connect 144hz external monitor to a gaming laptop with 60hz screen only, I already give a try and test it to my nitro 5 gtx1060 laptop (which is just 60hz), as long you fullfill the following requirement (from my online research and my own experiment):
the monitor support 144hz over hdmi (which have 1.4 or higher like 2.0 port ) Note: some manufacture have 1.4 hdmi port on the monitor but just lock it to 120hz only, be carefull to choice ur monitor and please read the full specifications.
your laptop or your gpu have 1.4 or 2.0 hdmi port.
your hdmi cable is 1.4 or 2.0
From my real test, I bought a monitor is Acer KG241P biip that have 2.0 hdmi port (its engraved on the back of monitor close to the port), and it included with the 2.0 highspeed hdmi cable on the package when im unboxed it, its plug and play to my laptop acer nitro 5 GTX1060 (60hz only from factory), and the 144hz setting instantly appear on my acer monitor..
U can buy the same monitor for ur laptop, make sure that u buy the acer KG241QP 144hz included HDMI highspeed cable inside the box.. some acer monitor included with displayport cable..
Thats it my real experience,
The other monitor that I know support 144hz over hdmi(from my online research) is Viewsonic XG2401 and and Viewsonic XG2402 (but note : i never test the viewsonic monitor)