How to find mixing ratios in a mixture model with known parameters?

This question does not ask for a formal solution or rephrasing, but for a practical implementation. That is why I am asking here and not on [cross-validate](https://clustering stats.stackexchange.com)

Let us assume I have $y$ observations and a mixture model of $g$ Normally distributed components with mixing ratios $\lambda$ and I know their parameters $\theta$. How can I estimate only the ratios $\lambda$ and not the parameters $\theta$?

So far I have only managed to estimate the entire mixture model, meaning $\lambda$ and $\theta$. But as all my observations come from the mixture and I have a prior guess about the parameters I really would like to find the ratios $\lambda$.

So far I have had no luck with the R packages mclust and mixtool. It might be that these packages are not appropriate or that I could not figure out how to use them the way I want to. I would also be open to other suggestions. Any insight would be greatly appreciated.