what do you mean by “LU rate” ? Do you mean the ratio of SDCCH allocated for location update / SDCCH allocated (LU + SMS + Call + SS + IMSI DETACH + …) ?
Or do you mean the LU success rate ?
How do you compute the success rate ? Nb of LU requests / LU accept ?
If a LU is rejected, it is done by the HLR itself, either the MS is not allowed to be in this network, or the MS has been disconnected (NSS timer expiry “implicit detach”).
Since you said that you disabled national roaming, when a MS tries to “IMSI ATTACH” on your network, it actually sends a LOCATION UPDATING REQUEST with the cause “IMSI ATTACH”.
This IMSI ATTACH failure is therefore counted as a LOCATION UPDATE failure.
In order to analyze this issue, you can simply perform a drivetest with a MS from another operator, in a zone that is not covered by this operator. See if this MS is attaching to your network or not.