The phrase is only a 'status' used by the CFMU and presumably your Ops Controller is jumping to conclusions based on a lack of knowledge as to what it means.
Most flights just have a normal status or one referring to the last message type issued by CFMU to the flight, but as you found out, some can have a 'Late' code assigned to them.
LF for Late Filer (FPL filed with less than required time stated in AIP - 3 hours normally)
LU for Late Updater (Change to EOBT filed late - I believe this is less than 20 minutes before EOBT)
LFU for Late Filer and Updater (FPL filed late and then changed late)
As others have said, if any of these status messages apply to your flight, you will be automatically given the next available slot. The CFMU automatic system primarily works on a 'First Filed - First Served' philosophy. If it's busy and the airspace is already experiencing heavy demand, your revised CTOT could be some significant time in the future as that's when the next available slot will be. Everyone else filed in the system, and now deemed ahead of you in the slot allocation process, have already taken all the others. The LF, LU, or LFU status will show Network Managers the reason for your excessive delay, and may trigger them in to improving things for you, if they can. Other aircraft slotted within your Regulation changing their status with CFMU can also free up slots which can bring your CTOT significantly forward. With a Ready message from the Aircraft Operator or Departure ATC, this is much easier to manage as they know that the aircraft can be got airborne relatively quickly if a gap becomes available in the slots.
Filing a complaint is pointless, simply because CFMU have been complying with the rules, however, your Ops Controller should be aware that CFMU have a Help Desk which they can contact to find out more information (if they don't understand what is happening or terminology) or to discuss what might be done in the way of assistance in improving things for an individual flight experiencing excessive delay.