It’s called “whip’ and is common on long lead screws driven at speed. One method that is used to reduce it is to put the lead screws under tension using tension nuts and thrust bearings.
This is my set-up - outer side of the plate with tension nut and thrust bearing
The inner side of the plate just uses a conventional locking collar
This problem is one of the reasons that the more expensive ball screws are used.
There are formulae online that you can use to calculate the maximum speed you can drive a lead screw of a certain length and root thickness. Thicker lead screws allow you to run your CNC faster and reduce “whip”.
In addition:
During normal operation ie. cutting, it shouldn’t be a problem as the lead screw speed is slow - you normally only see it when travelling at higher speeds.