I have used two metods to stop oscillation.
1, inserting lossy elements in parallel with inductors in the power chain, for example, adding low value resistors to reduce the Q of the bias tee inductors,
2.) using flexible RF loss antistatic foam, you can attach it to copper tape (on its back) and then put a thin piece of cellophane wrap right on top of the circuit and press the antistatic form over that. Apply some pressure right on the device. This will introduce loss.
3.) make sure that both the input and output to the LNA go through a short length of decent 50 ohm transmission line, ideally where the shielding is well grounded. Ferrites around these two short lengths of transmission line may help too, all my gain stages are festooned with as many ferrites as I can reasonably fit on them. This may look funny but my experience is that it pays off in signal integrity.
4) Make sure the grounding on the MMC is top quality. It should be immediately under the MMIC, for example, place your vias right at its legs. Make sure the impedance of the vias is low. Grounding is the most important thing with newer 50 ohm LNA devices. They are super easy to use if you give them what they want.