I'm not sure if the Mayor means the City shouldn't bring some of its workers back, or that the City can't. If the former, from the City's perspective, the Mayor might be right. If he means the latter, he's almost certainly wrong.
Partial revocation of the lockout - bringing some workers back to work while other workers remain locked out - is a tactic that would be open to the City. Nothing in The Saskatchewan Employment Act says that a lockout can't be partially or fully revoked by an employer. The City could move from a total lockout of all transit workers to a partial lockout of just some of them; just as it could have done the reverse, locking out some workers and then moving to a full lockout later.
The parties could also negotiate a deal for some workers to return, as happened in 2007 - during a strike, not a lockout, but the principle's the same - when striking members of SGEU agreed to return to work to operate snowplows during a terrible blizzard (as recounted here).
Similarly, strikes need not involve all striking workers at all times. The "rotating strike" is a tactic of long standing in labour relations - not that long ago, members of the Health Sciences Association of Saskatchewan used rotating strikes during their dispute with their employers back in 2011 (as mentioned here).
(The interaction between rotating strikes and partial lockouts can get pretty damned complex. See, for instance, the scenario that played out in B.C., where the B.C. Teachers Federation commenced rotating job action and the employer retaliated with a partial lockout, briefly summarized here.)
In theory, in the context of a strike, striking workers could even walk off the job en masse and then, some time later, have a number of them propose to return to work. It's difficult to see what advantage this tactic would have for a union (I don't see how it could do anything but doom the strike to failure), but it's something that could be done.
But in either case, the other side doesn't have to accept it. An employer faced with rotating strikes could impose a lockout. A union faced with a partial lockout (or partial end to a lockout) could call a strike. (The ATU got a 90%+ strike mandate from its members earlier this year.)
But the main reason why it's not common for an employer (in the case of a lockout, as we have here) or workers (in the case of a strike) to "downgrade" from a total lockout or strike to a partial one is that it can drastically reduce bargaining power..
In the case of a strike, workers' bargaining power comes from their ability to "vote with their feet" and withdraw their labour. Pressure on the employer comes from the fact that - barring the use of "replacement workers", which is a whole other story - the employer's operations are shut down. In the private sector, that hits the pocketbook. In the public sector, it causes public unrest and political pressure. So the union's strength comes from the strength of the withdrawal, and a partial return to work is usually going to weaken that position. In fact during protracted strikes some employers do try to lure striking workers back to work in order to weaken the strikers' resolve and lessen the impact of the strike. "Solidarity" is the watchword of the labour movement for a reason.
But in the case of a lockout, it can weaken an employer's bargaining position, too. It can make the employer look hesitant - if a partial return-to-work is needed, why did the employer impose a total lockout in the first place? Is the employer really ready for a protracted labour dispute? And lifting the lockout on some workers would reduce financial pressure on the locked out workers and on their union's resources. (The fact that some workers will remain locked out would still be an issue, of course - nothing says an employer would have to allow all locked out workers an equal opportunity to return to work - but there are ways to deal with that, on the union side.)
It also sends the ball back into the union's court; the union would now have the option of calling a strike - pulling whatever workers were back on the job - at a time where the union would be at an advantage.
But all of that being said, there's no question the City could implement a partial return to work. (It could just voluntarily end the lockout entirely, too, but that doesn't seem very likely.) It could try to negotiate terms of a partial return to work with the ATU (which, from the City's perspective, would certainly have to include a no-strike promise from the ATU), as Councillor Hill suggested he might try to do. There are reasons why the City might not want to do so - and reasons why the Union might not want its members to return.
But "you're either in a lockout, or you're not" is a very simplistic way to look at this situation, and it's misleading to suggest a lockout - or a strike - has to be an all-or-nothing affair.
And of course there's still the question of whether the lockout is legal in the first place, which would render much of this moot. The City seems to be hunkered down and waiting for the decision of the LRB before it makes any new moves.
(As an aside, it rings a bit hollow for Mayor Atchison to say that City Council "gives direction" but does not get "involved in negotiations", given that it was City Council that voted to make unilateral changes to the municipal pension plan. Attempting to pass the buck to the City's human resources department (or legal department) is poor form, in my opinion; does
[I had originally referenced City Council in the above paragraph, but since it's the Mayor who said it, it seemed unfair to tar all of Council with the same brush. If any Councillors have made similar comments, I'd make the same comment about them, obviously.]