Nomakhaladi Silaza, 47, and her daughter Nomakhwezi Silaza, 23, who was a Walter Sisulu University student and set to be the family's first graduate, died in the tragic incident.
Two other children from the Silaza family were injured and taken to hospital.
The family of seven lives in a two-room mud house and is struggling to raise funds to bury their loved ones.
Family spokesperson Thembelani Mnguni said they cannot afford the funeral costs.
"We were hopeful that Nomakhwezi would graduate and lift this family out of poverty, but she has now passed away. The lightning storm struck the goats first, then entered through the window and hit those inside the house," Mnguni said.
Zilindile Hibanaa, councillor for Ward 20, said he was shocked by the family's living conditions when he visited after the incident.
"I was horrified. This family urgently needs help to bury their loved ones. I have contacted disaster management to assist them," he said.
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