Is there anything I can do to prevent my lazy eye from drifting?

An eye that drifts. When tired will also drift when drinking alcohol. Other than avoiding these things, if the drifting is frequent, surgery can help.
Depends on your age. The younger you are, the more options are available. Glasses tend to be the mainstay in young children, as is surgery. As you get older and your brain "decides" not to use the vision from your lazy eye, it tends to cause it to drift out of the way. Correcting the eye's position may work, but only temporarily.