Quick example of how you could extract ID variable from LME formula

ExtractIDvar.R

#Function to extract the cluster ID variable from a formula
get_id <- function(formula){
    
    #Extract the thing between the | and the ) in the last part of formula
    #This is the clustering variable
    idvar <- gsub('.*[|](.*?)).*','\\1',formula[-c(1:2)])
    
    #Remove white space
    idvar <- gsub("^\\s+|\\s+$", "", idvar)
    
    #Return
    return(idvar)
}

#Example use
get_id(formula = y ~ (x + z | id) )