It depends on the exact application. Lithium battery grid storage project parameters vary greatly, with discharge ratings being anywhere from 0.1C to 4C, with the majority being below 0.5C.
List of energy storage projects - Wikipedia
Automotive batteries should easily be able to handle those <0.5C projects, especially if they limit the SOC window more than in their EV application -- which they very likely would to increase longevity.
(If a utility is looking to shave peak demand for just a short amount of time on the highest demand hours of the year, they might want an installation with relatively small energy capacity but with a high power rating that discharges all of its usable energy in less than an hour.
But if a utility wants to shift demand, like they'll have to do more and more as solar becomes a larger part of the energy mix, then they'll want larger-capacity installations that discharge over a number of hours. These types of projects are the ones likely to dominate in the future.)
Here's a decent (if dated) piece on the different chemistries Tesla was considering using in different storage applications:
Tesla will use different batteries for its grid products. Here's why