Lussick completed a mid-season switch from St Helens as the Eels sought cover for English international Josh Hodgson.
Former Canberra captain Hodgson has suffered a neck injury which could spell the end of his career.
Arthur, who confirmed Hodgson wouldn't play again this year as he weighs up a medical retirement, said Lussick would rotate No.9 duties with Brendan Hands on Friday.
There is no chance for Lussick to ease himself back in as Parramatta aim to keep hold of a spot in the top eight against a Melbourne side stinging from a humiliating loss to Newcastle.
"Joey was a good fit for us and when he left the club, we didn't really want him to leave," Arthur said.
"He didn't really want to go either but financially it was a better situation for him to go overseas.
"He's glad to be home and knows the style of footy of how we play and what we like and don't like.
"He plays a pretty tough job and keeps it simple and his service is excellent."
Lussick's return comes at a welcome time for the Eels with Shaun Lane (elbow) joining Hodgson (neck) and the suspended trio of Dylan Brown, Reagan Campbell-Gillard and Maika Sivo on the sidelines.
The Storm will also be without Nelson Asofa-Solomona and Reimis Smith due to injury, while centre Justin Olam has been dropped but Arthur said their absences would count for little.
"They're resilient and it doesn't matter if you've got blokes out you know you've going to get the same style of footy from them and you have to be prepared to fight hard for the full 80 minutes," Arthur said.
"I don't need to stress that with our players because I feel like over the last four or five years our guys know what sort of contest it's going to be and and they come prepared for that."
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