To convert inferential statistics results from a Linear Mixed Effects (LME) analysis to an effect size, specifically to a dd value, the following online effect size calculators may be utilized:

Psychometrica Effect Size Calculator:

This calculator enables the input of various statistical values (e.g., t-values, F-values) for the computation of effect sizes, including Cohen's d.

The ESCI Effect Size Calculator (Exploratory Software for Confidence Intervals) is a comprehensive tool developed by Geoff Cumming that can handle various statistical inputs and provide effect size estimates, including Cohen's d.

The Effect Size Calculator by Daniel Lakens is a straightforward calculator that can convert different test statistics (e.g., t-values or means and standard deviations) into Cohen's d.

There are several ways to do this depending on details of design, your goal and so forth. If you just want to scale a difference in means in standard deviation units l’d argue that the simplest and cleanest approach (which is easy to explain) is just take the coefficient for the mean difference (assuming dummy coding or an equivalent like -0.5, 0.5) and divide it by the sd of the y (outcome) variable calculated on the raw data. This answers the question how big is the difference in my model on the scale of sample sd of the outcome.

Of course this isn’t Cohen’s d because that’s defined as the population difference divided by population sd in a two independent group design. You don’t have that design or else you wouldn’t be using a linear mixed effects model - presumably with other predictors etc. However, it is a standardised mean difference in the spirit of d. If you do report this or something else please explain how you calculated it. It’s common to see d reported for designs with designs for no agreed/consensus method for calculation and no explanation. In my view that’s worse than not reporting d. Actually just reporting the estimate in the original units is a valid approach and arguably more useful than d (which has issues and may well be just an ad hoc quantity unrelated to Cohen’s d).

It's not that straightforward to get a Cohen's d -like effect size statistic for a model like this, even if you're working with the original data.

But if you mean "inferential statistics", like you only have a p-value, then I'm not sure there's much you can do...