Is it possible to have a thickness / liquid in the uterine lining other than cancer for a woman who is going though or has been through menopause?

Uterine lining . Yes! by far, an endometrial polyp would be the most common cause of those ultrasound findings. Infections can also cause the findings. If there is bleeding/spotting, then cancer is present about 20% of the time.
Yes, but... Decades after menopause, i've seen old polyps or old thickened cystic endometrium. If there is any concern, a biopsy is a simple procedure. I wish you luck.