Lulia's haul matched the Tigers' record mark held by Kevin McGuinness and Marika Koroibete.
The Tigers jumped to ninth place on the ladder on 22 points, only outside the top eight on for and against, to get their season back on track after breaking a two-game losing streak.
The second-placed Bulldogs will have a nervous wait ahead of the release of the NRL match review panel findings with halfback Trent Hodkinson on report for a lifting tackle on opposite number Luke Brooks.
Josh Jackson could also find himself in hot water after he was reported for a deliberate trip on Moses.
Following a frenetic opening 25 minutes, which included six tries, Canterbury held a 18-16 lead at halftime.
The Bulldogs took first blood when Krisnan Inu went over in the corner the play after Mitch Brown split the line open.
Brown went from zero to hero very quickly when he produced two mistakes which led to Tigers tries.
First he spilt the ball off the kick-off and the Tigers levelled things up through Bodene Thompson.
The Bulldogs No.1 then knocked on on the tryline with Lulia scoring the next set.
The Dogs took back the lead with two tries in four minutes through Tim Lafai and Corey Thompson.
When Lulia crossed for his double, the Dogs' advantage was reduced to just two.
Brown's horror day continued after the break when he spilt it off the kick off, Lulia grabbed his third the next set and the Tigers never surrendered the lead.
In the second half, Moses broke the game open, putting in a deft kick for Curtis Sironen, setting up Lulia's fourth before putting his former schoolmate Brooks over.
The Tigers iced the game with four-pointers to Aaron Woods and James Gavet.
- AAP