Cuthbert and Williams missed Wales' back-to-back clashes with England, but the two backline players have been passed fit and in contention to start against the Springboks as they bid for a place in the 33-man squad to be named on August 21st.
But there are concerns over the availability of Lake and new loose forward Taine Plumtree for the World Cup in France.
Lake went off early in Saturday's defeat by England at Twickenham with a knee injury while Plumtree damaged his shoulder as he won only his second cap.
The new skipper looked emotional on the sidelines after coming off after 26 minutes and has had a torrid time with injuries over the last 12 months, including missing the Six Nations earlier this year with a knee problem.
Wales can ill afford another setback as they are short of quality hookers. Ken Owens is out of the World Cup with a back injury and last week Ryan Elias was forced off after six minutes with a hamstring problem as Wales beat England in Cardiff.
Loose forward Taine Basham must undergo a series of head injury protocols after he failed a Head Injury Assessment (HIA) test following a high tackle by Owen Farrell, which saw the England captain dismissed.
