Of course they will need to work to bring their fans back. They just basically threw away more than half of their season over petty squabbling between grown men over money, when most people involved make at least several hundred thousand a year. And that's the low end people. They cost their local areas tens and possibly hundreds of thousands of dollars in revenue. There is lots of work ahead for the NHL.
The NHL is not other leagues, and they do not really have to act like other league. The casual fan will follow whatever flavor of the month league is in session. The NHL has the luck of having the most hardcore fanbase, and as a result don't really have to work to win them back. They never left.
The NHL really does need to stop screwing casual fans over, but majorly dedicated hockey fans are what they are, and if there's a game on the ice to be watched they will do so. They're (completely understandably) pissed off but the NHL is in no danger of losing their attendance.
The NHL has some of the most loyal fans there is. They are probably more loyal than the majority of professional sports fans. Due to this, I do not think that the NHL will have to work to get back their fans. Most of them will come back without hesitation.