With lapply you can operate the rollapply function on each column resulting in 
    acf series for the selected lag value. We then use Reduce to combine results from the above step.
I have used dataset edhec from PerformanceAnalytics package for this demo. You
    can change the width parameter accordingly.
library("PerformanceAnalytics")
#load test dataset
data(edhec,package="PerformanceAnalytics")
#select subset with fewer columns
edhec_sub = edhec[,1:5]
fn_lag_ACF = function(lagValue = x) {
#for width as 1 year calculate acf for input lagValue for each column
acfList = lapply(edhec_sub,function(x) {
 TS = rollapply(x, width = 12,
 FUN = function(z) acf(z,na.action=na.pass,lag.max= lagValue,plot=FALSE)$acf[lagValue],
                by.column = FALSE, align = "right")
 colnames(TS) = colnames(x)             
 return(TS) 
})
#combine acf output for all columns from above step
acfMerge  = Reduce(function(x,y) merge.xts(x,y), acfList)
return(acfMerge)
}
#test with lagValue = 2
lag2DF = fn_lag_ACF(lagValue = 2)
Output:
head(lag2DF,15)
#           Convertible.Arbitrage CTA.Global Distressed.Securities Emerging.Markets
#1997-01-31                    NA         NA                    NA               NA
#1997-02-28                    NA         NA                    NA               NA
#1997-03-31                    NA         NA                    NA               NA
#1997-04-30                    NA         NA                    NA               NA
#1997-05-31                    NA         NA                    NA               NA
#1997-06-30                    NA         NA                    NA               NA
#1997-07-31                    NA         NA                    NA               NA
#1997-08-31                    NA         NA                    NA               NA
#1997-09-30                    NA         NA                    NA               NA
#1997-10-31                    NA         NA                    NA               NA
#1997-11-30                    NA         NA                    NA               NA
#1997-12-31             0.5560540 -0.3010264            0.02908761        0.3305791
#1998-01-31             0.5055951 -0.4245876            0.04278214        0.1761287
#1998-02-28             0.5195872 -0.4298767            0.01375580        0.1605579
#1998-03-31             0.5070003 -0.4656213           -0.04519778        0.2061610
#           Equity.Market.Neutral
#1997-01-31                    NA
#1997-02-28                    NA
#1997-03-31                    NA
#1997-04-30                    NA
#1997-05-31                    NA
#1997-06-30                    NA
#1997-07-31                    NA
#1997-08-31                    NA
#1997-09-30                    NA
#1997-10-31                    NA
#1997-11-30                    NA
#1997-12-31           -0.11842164
#1998-01-31           -0.05986578
#1998-02-28           -0.09663855
#1998-03-31           -0.09680819