子子子子子子子子子子子子 is a different category: in Japanese, Chinese characters usually have multiple possible readings. In the case of 子, it can be read as ko, ne, shi,

子子子子子子子子子子子子 is a different category: in Japanese, Chinese characters usually have multiple possible readings. In the case of 子, it can be read as ko, ne, shi, or ji. 子子子子子子子子子子子子 is a word play that switches between them. It reads neko(no)kokoneko shishi(no)kokojishi. Note the no are omitted, which would be unusual here (although there are cases of all Chinese character sentences, but they are plain Chinese read as Japanese, with Japanese grammar made up on the spot). The actual correct way to write that sentence is 猫の子仔猫、獅子の子仔獅子.