How can I compare results across different SEM programs?

You can compare the likelihood of the model estimates given the data across different programs.
Lavaan and Mplus state the logarithm of the likelihood (Loglikelihood, H0 Value) whereas
Onyx states twice the negative loglikelihood (“Fit” in estimation panel).
To compare the results, you have to multiply the loglikehood given by Mplus or lavaan by -2.
In this metric, the likelihoods should be the same. If they differ, the lower value is the
better set of estimates.

In lavaan, for an estimated model obtained by the command “fit <- sem(...)", the twice the negative likelihood is obtained by the command: -2*logLik(fit)[1]