LSO was using a VHF system, one for dispatch and one for talk-around purposes. I don't recall the exact frequencies, but seems to me that they were in the 154-157 range. Of course they had 39.9 as well, but that was used more by smaller towns to contact the Sheriff's office or NSP.
I recall working as a Marshal for Eagle, we had only 39.9 in our vehicle and called LSO more often than Plattsmouth Sheriff because we were on the fringe of their reception, and could talk to Lincoln Sheriff with no problems.
The sheriff's office then moved over to a system shared with LPD still on the 460MHz range sometime in the late '70s for dispatch purposes, and kept their VHF frequencies for other needs. This was apparent on LPD radio when you heard a unit calling in as 902xx, the 90 identified used to identify as a sheriff's unit.
I hear to this day units calling in as 903xx, which one would think would be Gage County sheriff's office, but I don't believe that to be the case, rather I believe these units to also be LSO units, either Corrections when transporting, Reserve units, or Courthouse security. I just haven't gotten these units figured out yet.
As an aside, you will also hear US Marshals on LPD radio, identified by the call sign US2xxx
Hope this answers your question.