I understand 'dictated by' but what does it mean by 'dictated to by'?Secondly,'lot at the mansion' is understood but 'up at the mansion' again confuses me.
I will not be dictated to by that lot up by the mansion.
by that lot is a prepositional phrase. It gives you the agent of will not be dictated to, which is a passive construction.
at the mansion is is a prepositional phrase showing where that lot is located.
up means "in a high position." (Cambridge). You can take it out of the sentence and the sentence would still be grammatical. Or the sentence could have a different 'directional' word such as over or down.
Up means that the lot at the mansion are somehow higher than the speaker. A typical meaning would be that the mansion (the whole mansion) is at a higher altitude than where the speaker is, or where the speaker usually is. Down at the mansion would mean the opposite. See Definition 1b, and the example sentences of 1b, in the Merriam Webster Learner's Dictionary.