I have to wonder if there is not a deeper quandary behind your question. The fundamental equation in SEM is Sigma^ = Sigma(theta) meaning that the implied moments are those implied by the model given parameter values as arguments. The idea is that the parameters on the right-hand side explain the moments, such as correlations, on the left-hand side.
It seems as if you are trying to put a correlation or covariance on the right-hand side as a parameter. This can be done for convenience in simple cases, but it is generally not explanatory to place correlations or covariances on the right-hand side (in the model). These are often interpreted as shorthand conveniences for implicit latent variables with affects on both the variables involved in the residual covariance.
If you are just interested in the correlations, you can obtain these using lavInspect() and choosing what='cor.all'. This will give you model-implied correlations between all variables, latent and observed.
If you are looking for a substantive interpretation of parameters, it may help to think of the residual/disturbance/uniqueness for a variable in the model as a separate latent variable with its own substantive interpretation. One way to think of it is as a linear bundle of the omitted determinants of the value for that variable. You can then interpret the correlation or covariance between the residual and any other variable as an association with that bundle (rather than as a correlation with the variable as whose residual that bundle serves).
In terms of lavaan syntax, in a sense x ~~ y means something different depending upon whether either x or y is an endogenous variable. You can obtain a unified interpretation but not by trying to assimilate the endogenous case to the case where both are exogenous. Instead, think of the exogenous case as a special case in which the residual variable happens to be coextensive with the exogenous variable to which it is attached (because there are no other causal variables). Understood that way, x ~~ y always refers to a correlation between latent variables representing the residuals of x and of y.
I could be missing something but I hope that helps.
Keith A. Markus
John Jay College of Criminal Justice, CUNYhttp://jjcweb.jjay.cuny.edu/kmarkus
Frontiers of Test Validity Theory: Measurement, Causation and Meaning.http://www.routledge.com/books/details/9781841692203/