I'm running a development branch so things may have changed, but the results class returned by MixedLM.fit() should have an attribute called 'llf'. That is the value of the log-likelihood function at the estimated parameters. If you have two nested models and take -2 times the difference in their llf values, under the null hypothesis where the simpler model is true, this will be a chi^2 random variable with degrees of freedom equal to the difference in degrees of freedom for the two models.

Note that many people feel that you should switch the estimator to ML (not the default REML) when using LR tests.