Arthur is a member of the Mystery Skulls and an excessive coward.His character is heavily based on Shaggy from the American animated television series Scooby-Doo.
Aside from this he seems to be rather friendly and good-hearted.Before Lewis' death he was shown to be jealous of his friends' relationship.Later on he is too terrified to try and set things right.Arthur and Vivi are part of the same paranormal investigator group.They are portrayed as mutual friends and appear to worry about each other's well-being (Vivi tries to defend him when he's cornered by Lewis and Arthur tugs her out of the mansion and shoves her into the van when they are making their escape).
Before Lewis' death Arthur seemed to be unhappy with Vivi and Lewis dating.
Because of this most people assume that he has/had feelings for her.
Mystery is another member of the Mystery Skulls (as well as their mascot). Mystery was the one who saved Arthur from being entirely consumed by whatever was lurking in the cavern and possessing him the night Lewis died.
In order to save him, the dog tore off one of Arthur's arms which is replaced by a robotic arm in the present.
Lewis was a member of the Mystery Skulls before he died.
Back then him and Arthur were team members and, most likely, friends.