The Bafana boss roped in Kaizer Chiefs keeper coach Lee to help the national team prepare for Saturday's 2019 African Nations Cup qualifier with Libya in Durban after Andre Arendse withdrew at late notice for family reasons.
The Brit subsequently dismissed suggestions nepotism was in play, insisting it makes sense given the time constraints and that Lee has worked with Williams and Khune in the past.
Lee previously coached Williams at SuperSport United before linking up with Khune at Amakhosi in February.
Baxter also labelled his son the most qualified goalkeeper coach in South Africa "by a country mile".
"Obviously they [SAFA management] spoke to myself and Itu because we've worked with him and we obviously kind of mentioned him," said Williams, who is also in competition for the Bafana number one jersey with Bidvest Wits' Darren Keet.
"He's very good goalkeeper coach. He doesn't just focus only on us ... he focuses on the defence as well. So it's good for us that he's here.
"Sadly it's only Darren who hasn't worked with him, so it's good for myself, Itu and Darren.
"We are learning a lot from him. He's from Europe and we are just happy to have him here."