I've recently installed a Luvay Piezo Acoustic Pickup on my guitar, and I don't have an amp at home. Is there any way I can plug it in to my laptop?
Not without purchasing some additional hardware. At the very least you would need something like this: https://www.sweetwater.com/store/detail/GUITAR2USB--behringer-guitar2usb
You will also need some audio software for accessing the sound of your guitar. There may be some built in audio software in your computer. If not you will also need a DAW (digital audio workstation) of which there are some free options for PC and Mac.
I am not endorsing these products, I’m just using them as an example. There may be an impedance issue since piezo pickups are very high impedance in general and the computer interface may not be designed to handle it. The pickup and interface specs for impedance should be within the same range for the best sound. If you do buy something make sure they accept returns just in case it doesn’t work out.