The High-Luminosity LHC will start operations for physics in 2030. The expansion of the dataset will be achieved by increasing the instantaneous luminosity of the LHC to 5-7.5 times its design value. For the ATLAS Liquid Argon calorimeter system, this poses new technical and operational challenges due to the higher radiation doses for the front-end electronics and increased pile-up caused by coincident and consecutive collisions. Additionally, the trigger rate of the first-level hardware trigger is projected to be increased to close to ten times its current value. At the same time, two new trigger subsystems must be provided with reconstructed energy data up to cell-level granularity in real time. To keep up with these conditions and requirements while not sacrificing data quality, the Liquid Argon calorimeter readout needs to undergo a fundamental upgrade. The new off-detector electronics will be realized on custom ATCA-compliant boards based on FPGAs. A total of 278 new signal processing boards will receive the digitized data from 182468 calorimeter cells at 40 MHz. They provide enough resources to facilitate the use of new online energy reconstruction algorithms and transmit the results to trigger and DAQ systems. A new timing system consisting of 30 additional ATCA blades will complement the new on-detector electronics by providing timing, monitoring and control functionality. This article gives a summary on the planned off-detector electronics upgrades and the recent progress in firmware and hardware development.