Yes. In fact, the Nazis appear to be the only people to have ever used phenol for executions.
Primarily, the purpose of using lethal injection is to reduce suffering and "sanitize" the process of executions. If he protocol for administering these drugs is inadequate, lethal injection can cause great pain and be very drawn out. Phenol was used primarily as an antiseptic during this time period.
The antiseptic properties of phenol were used by Sir Joseph Lister (1827–1912) in his pioneering technique of antiseptic surgery. Lister decided that the wounds themselves had to be thoroughly cleaned. He then covered the wounds with a piece of rag or lint covered in phenol, or carbolic acid as he called it. The skin irritation caused by continual exposure to phenol eventually led to the substitution of aseptic (germ-free) techniques in surgery.
Phenol is the active ingredient in some oral analgesics such as Chloraseptic spray and Carmex.
Because phenol was not very effective in causing swift death, the Nazis injected it into the ventricles of the heart. (In other words, its an unusual choice)
The first execution using lethal injection after WWII was in Texas in 1982 using a more effective three drug protocol. Alternatively, other countries use overdoses of barbituates.