I use eye drops to relieve the dryness and sea buckthorn to reduce the problem. Also, my optician recommended doing very gentle circular movements just under the eye using the ring finger (so as not to apply too much pressure) ending with an upward movement as apparently this encourages lubrication of the eyeball? I don't do it very often though as it feels really horrible.
I think dry eyes must be a very common symptom of menopause, as when I had my last eye test, she was very concerned by the 'abnormal' dryness and was planning to send me for more tests to find out what the problem was - but as soon as I said I was perimenopausal, she said that would be the cause, so no need to worry and just gave advice on how to manage it (drinking lots of water is another important thing. Also cutting down on caffeine) .