The constant $c$ is commonly referred to as the speed of light, but really it's better interpreted as a conversion factor between distance and time units, or a maximum speed of cause and effect. The speed $c$ is the only one that observers in all frames agree on. Therefore if we found that the speed of light was not $c$, then observers in different frames of reference would not measure it to be the same. In particular, there would be some frame in which is was zero. This would be a preferred frame of reference. Having such a preferred frame is one way of breaking Lorentz invariance.
Theoretically, adding a vacuum energy term in general relativity does not break Lorentz invariance, and therefore we can be sure that it doesn't change the speed of light. This makes sense because the role played by vacuum energy in general relativity only becomes apparent on very large scales. This is why it was originally called a cosmological constant.
Experimentally, Lorentz invariance is one of the most precisely tested physical claims in all of history, and all tests have come up negative.
