Alivia is a channeler that spent hundreds of years mastering combat in a land with sporadic combat. Likely, most of her knowledge involves battlefield weaves, though I'm sure that by modern standards, she can defend herself. She probably, however, has never faced anyone approaching her strength in the power, or her skill.
Lanfear - spent the better part of a century as one of the most prominent figures during a massive world war. She not only had to contend with the enemy trying to eliminate her, but her allies as well. She has faced Both men and women whose strength, skill, and knowledge rivalled her own and came out at the top of a very short list.


To sum it up: Is it believable that Lanfear could overcome Alivia's strength and ter'angreal advantages? Very much so.