There's really no way that this is possible. Mayo is going to want more than Courtney Lee. Not only is it impossible to straight up sign him for that, it'd be very difficult to even to put a S&T package together for what would likely be at least 6-8 million per year.
It isn't completely impossible to S&T for him. Difficult, but not impossible.
Suppose this:
Dooling, signed for $2,695,680 (the max he can be signed for per the base-year compensation rule)
Sean Williams (non-guaranteed for $915,852)
E'Twaun Moore (non-guaranteed for $762,195)
$3 million cash to pay Memphis for taking Dooling
whatever draft pick necessary to facilitate Memphis helping out
If this trade is consummated after KG, Green, and Bass officially sign, but, before JET signs, and we renounce all of the free agents we've never renounced (with Krstic being the only one of even existential value), we will be under the tax after the trade is completed, which allows us to take back 150% + $100,000 of the salary we traded. That would allow us to pay Mayo $6,660,591 in year 1 of a deal, and give him 7.5% raises, instead of 4.5% which he'd get if he doesn't find a new team via S&T.
Furthermore, because the Grizzlies are over the cap/in tax land, the most Mayo can be S&T for by any team is $6,759,164, which is around $100k more than the above proposal. So, assuming Memphis is willing to help, we can do pretty well by having them take on only $2.7 mil in guaranteed contracts, and they need combo guard depth anyway, so Dooling is a decent fit in that regard.
Do I think they'll do this? No, not really, because in general I expect all the other possibilities to happen. But the C's can make a competitive offer to Mayo.