Here is the sentence spoken by Kansai speaker.
Other than the question I put on the topic, if the 「の」 is not used instead of 「を」, I would like to know if I can omit the 「の」 in the sentence?
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This has nothing to do with Kansai.
「フォークみたいの」 means 「フォークみたいなもの」= "fork-like thing".
The 「の」 is not being used instead of 「を」. Rather, 「を」 is being omitted because of the informality of the speech.
You can correctly say 「フォークみたいのを貸してください」 if you want to.
You cannot omit the 「の」 because if you do, 「フォークみたい」 cannot be nominalized.