There was a good talk about a month ago at the 2019 CCCamp on the limitations of general purpose SDR. And it focused on “Why an SDR board like a USRP or LimeSDR is not a cellular base station” https://media.ccc.de/v/Camp2019-10248-the_limits_of_general_purpose_sdr_devices (and the exact same same video is also at https://www.youtube.com/watch?v=JgRCvzTuGkE ). Which may contain the answer to your question.
The on-board clock for both the limeSDR-USB and LimeSDR-Mini are given as +/- 1 ppm initial, +/- 4 ppm stable. So my guess with almost zero knowledge about LTE would be that you probably need a more accurate external reference clock, something along the lines of : http://www.leobodnar.com/shop/index.php?main_page=index&cPath=107
And if you configure your external reference clock to be 30.72 MHz for the LimeSDR-USB, that would probably require the least effort.
ref: https://wiki.myriadrf.org/LimeSDR-USB_hardware_description#Clock_distribution
Or configure your external reference clock to be 40MHz for the LimeSDR-Mini (but you also need to make a hardware change to a mini to enable the external reference clock and (permanently) disable the on-board VCTCXO).
ref: https://wiki.myriadrf.org/LimeSDR-Mini_v1.2_hardware_description#Clock_Distribution the actual position of the resistor to move is detailed a bit clearer here Enabling External Clock on LimeSDR mini 1.2?