Yes, I have confirmed and checked that the lens is snugly fit in the lens tube. I have read that you can adjust the “Y acceleration” on the machine but since I am a new user for this laser machine I have know idea on how to adjust “Y acceleration” using the software.
To adjust the acceleration you would use Edit > Machine Settings. Find the settings for engraving, and adjust the Y acceleration there. Write down the original number, change one thing at a time, and test in between. When you make a change, click ‘Write’ to send it to the controller.
You can also adjust the Y speed used for engraving (try lower). It doesn’t look like an issue with belts or your lens. You could try lowering the X acceleration too - different axis, but some of the shake may be from that.