LF is large fowl.... not bantam.. standard size...
i just recently threw together chicks that were 2 months 1 month, and 3 weeks, and they seemed fine.. they were all very close in size, with the youngest being bantams and the middles being mostly bantams with a couple JG and the oldest group being LF and bantam/lf crosses.... i watched for a few minutes, and i think since all the colors wer so similar they didn't even notice all the newness... lol...
just put them together at a time when you will be around to watch them...
another thing you can try, put them together the first time on new nuetral territory so they're all a little confused...
i did this with a set of chicks once for some silly reason i had to put both sets in the bathtub... and one set was like 3 months and the other set only 1 month so a big size difference.. no picking on each otehr.. they stayed segregated, on opposite ends of the tub, but when i let them loose together in the pen later they were fine...
might be worth a shot.. put them in the tub together while you give the brooder a good cleaning....