How stupid are you - he was directly linked because it was his missing girlfriend. BF/gf is #1 suspect in those cases. He had no reason to lie - he created reasonable suspicion by lying, i.e. he didn't meet the reasonable man standard. Which led to probably cause.probable cause here would need to be linked to the actual thing they're investigating, and you don't get to make logical leaps like "well if he lied about pants, he must be lying about kidnapping someone"
His lie was a dodge to shut the door - and yes, probably to either run away or hide evidence.