An alternative approach to get standardization parameters would be to calculate them (again):

tmp <- monthly_retail_tbl %>%
  group_by(Industry) %>% 
  arrange(Month) %>%
  mutate(Turnover = log1p(x = Turnover)) %>% 
  group_map(~ c(mean = mean(.x$Turnover, na.rm = TRUE),
                sd = sd(.x$Turnover, na.rm = TRUE))) %>% 
  bind_rows()

std_mean <- tmp$mean
std_sd <- tmp$sd
rm('tmp')

Hi, one could capture.output from standardize_vec like this:

stdout <- capture.output(groups <- lapply(X = 1:length(Industries), FUN = function(x){

  monthly_retail_tbl %>%
    filter(Industry == Industries[x]) %>%
    arrange(Month) %>%
    mutate(Turnover =  log1p(x = Turnover)) %>%
    mutate(Turnover =  standardize_vec(Turnover)) %>%
    future_frame(Month, .length_out = "12 months", .bind_data = TRUE) %>%
    mutate(Industry = Industries[x]) %>%
    tk_augment_fourier(.date_var = Month, .periods = 12, .K = 1) %>%
    tk_augment_lags(.value = Turnover, .lags = 12) %>%
    tk_augment_slidify(.value   = Turnover_lag12,
                       .f       = ~ mean(.x, na.rm = TRUE), 
                       .period  = c(3, 6, 9, 12),
                       .partial = TRUE,
                       .align   = "center")
}), type = "message")

And save mean and sd values automatically:

collect_vals <- function(stdout, string = "mean: "){
  stdout %>% grep(string, ., value = TRUE) %>% gsub(string,"", .) %>% as.numeric()
}
std_mean <- stdout %>% collect_vals("mean: ")
std_sd <- stdout %>% collect_vals("standard deviation: ")