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It is actually from PE rather than an LSF limit.
LSF holds the jobid as a 64bit int. Half the bits represent the jobid, and half the array index. So normally you could have 2^31 jobs, and each job could have 2^31 array elements. However, PE holds the jobid as a 32bit int.
So when PE is enabled, we have to remap the LSF jobid to just be 32bit, with 10bits to store the index, 22bits to store the job id.
This means when PE is enabled, MAX_ARRAY_SIZE is 1000, and LSF_MAX_JOB_ID cannot be larger than 2^22-1 (4194303).
A hack would be to split the job ranges, so PE jobs get a base ID in the range 1 .. 2^22 - 1. and non-PE jobs get a base ID from 2^22 .. MAX_JOBID. However this would still mean that have PE job would already have a duplicate in your accounting database, so it does't really address the problem.