Riemann4abcd = Table[RiemannR[la,lb,lc,ld] * 
  RiemannR[Unlist[all4abcdpart[[i,1]]]]*
  RiemannR[Unlist[all4abcdpart[[i,2]]]],{i,1,Length[all4abcdpart]}]

Out[73]=

                  ab  cdef             ab  cdef
  {0, 0, R     R     R    , -(R     R     R    ), 
          abcd  ef             abcd  ef
   
              fab   ecd           fab   ecd
    -(R     R     R    ), R     R     R    , 0, 0, 
       abcd  e     f       abcd  e     f
   
              fcd   eab           fcd   eab
    -(R     R     R    ), R     R     R    , 
       abcd  e     f       abcd  e     f
   
             cd  abef             cd  abef
    R     R     R    , -(R     R     R    ), 
     abcd  ef             abcd  ef
   
               ab  cdef            ab  cdef
    -(R     R     R    ), R     R     R    , 
       abcd  ef            abcd  ef
   
            fcd   eab            fcd   eab
    R     R     R    , -(R     R     R    ), 0, 0, 
     abcd  e     f        abcd  e     f
   
            fab   ecd            fab   ecd
    R     R     R    , -(R     R     R    ), 
     abcd  e     f        abcd  e     f
   
               cd  abef            cd  abef
    -(R     R     R    ), R     R     R    , 0, 0}
       abcd  ef            abcd  ef

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