"Is it possible to love someone but at the same time not trust them?"
yes of course it's possible ......untill you know very good the person you have close !
but

(MY opinion) when some time pass ..and i already knew that person and i know for sure she /he (a person) lie to me many times .....well than love disappear ,maybe is strange for some of us ..,for me is so ! tha't mean i can not trust you anymore ... conseguence : there is no respect betwenn 2 people , so why love ? love is many things toghether , not just physical attraction !
"becareful what you do 'cause the lie becomes the truth"
"So take my strong advice, just remember to always think twice
(Do think twice)"
are a piece ...of a very famous song !