Kelly and Martinez are not viable options right now because neither is stretched out to start. In addition, Martinez missed almost all of spring training due to visa issues.
Lyons and Gast were called because the FO felt they earned it. Granted, they haven't been lights out, but under the circumstances, they've held their own. Plus, they're 3-0 combined.
The Cardinal rookie pitchers, not counting Miller, are 6-0. I can live with that.
If Lyons and Gast falter, there are plenty of other options that don't involve a trade.