Lower limits of difference, on average (6)
I believe the answer is:
demean
'lower' is the definition.
(I've seen this before)
'limits of difference on average' is the wordplay.
'limits of' means to remove the middle letters.
'on' means one lot of letters go next to another.
'average' becomes 'mean' (type of average).
'difference' with its centre removed is 'de'.
'de'+'mean'='DEMEAN'
(Other definitions for demean that I've seen before include "Stoop" , "Belittle; degrade" , "disgrace" , "Lower in status or reputation" , "make base" .)