I think "le" here refers to "she", because it is an indirect object (for "he" it would be "gli"). "PiacutA" refers to the direct object (what she likes). So, i believe we could say either "I believe that she liked (or "has liked") it." or "I believe that she liked (or " has liked") her. p.s: i am not italian though.
"he liked her/it" would be (lei) gli sia piaciuta. "She was pleasing to him (gli )" (I'm taking some license with translating piaciuta). "She" = (lei ) is unstated in the exercise sentence, but reflected in the feminine ending of piaciuta - however, it could also be a thing of feminine gender - "it pleased him".
Please can someone help me with the use of sia or guide me to a thread that does it well. Whilst it doesn't appear to be integral to the understanding of the sentence here, it obviously is. Google Translate says it's 'both' but then has a multitude of possibilites to accompany it. It seems to be sverything and nothing.