Is it permissible to marry the eldest daughter of one's maternal aunt if one was nursed by the maternal grandmother (the aunt's mother) for only three times? And do sin and blame fall upon the grandmother and mother if they lied about the number of feedings?

Only five breastfeedings prohibit marriage, so there is no objection to marrying your maternal aunt's daughter unless it is proven that you were breastfed five times by your shared grandmother. If that is proven, then it is not permissible to proceed with marrying her, even if the grandmother or mother testify otherwise, unless their side is substantiated by a preponderant evidence that outweighs one of the two conflicting proofs.