I am working for a company that has just been sold. We have a US citizen that has been working for the company on a temporary workers visa. Would his visa transfer to the new company? If not, would the new company have to have an LMO in place before hiring

If the company will remain intact, although under different ownership, then the existing work permit should remain valid. If the old company will be dissolved and a new company the employer of such an individual, then a change of terms application may be needed, which would be expected to require a new LMO (assuming this is applicable). A typical work permit is specific to employer and position (and typically location), so the questions is what corporate entity will be the employer going forward.