Yes, the LOD score is dependent on the sample size. Maximum likelihood is proportional to the data (set). LOD = log10(LR), whereas -2*ln*LR is interpreted like Chi^2 with 1 df (usually the two models only differ by 1 df). 

Dear Hazel, Also LOD and number of observed in the pedigree (if you are performing a linkage analyses ) are depended from type of population where you are working.  For instant, in genetically homogeneous  isolates that are usually small by total sizes Nt, if you ascertained a pedigree with aggregation of any chronic disease, you cannot collect such many affected and unaffected pedigree member as you can do in outbred genetically heterogenous population with large Nt and large pedigrees. But no problems with these populations differences because in genetic isolates you can get LODs with high values in the linked regions easier for time and effort. Just problems will have with differences in gene pool between these populations -as result -you will get some LODs in same s in different regions, i.e. will get inter-populations differences...But it is another problems that we can discuss later. if you are interested