Lady Macbeth has plotted this out carefully and diligently.
Can I use the word "plot" in such a way? I know most people would want to replace that with "planned", but I don't want to keep using that word.
Plot (out) is a verb, and its use in your example is grammatical.
I sense there's a instinctive doubt here in terms of whether to use 'plot' as a transitive verb, or 'to plot out' as a transitive phrasal verb. In my mind, to plot a line on a graph, to plot to kill someone (intransitive) indicate a more linear activity than 'to plot out', which gives more the sense of a mind map than a list; an expansive, more intuitively flowing plan, rather than a logical more linear one. There's a sense in which with 'plot', the verb is just echoing the meaning of the noun, but extending the capture of it in writing once the plot, or at least the individual steps which are being written down, have been more or less finalised, or that there's more certainty in relation to them; whereas 'plot out' implies that the writing down and the creation happen more simultaneously by comparison, with less certainty. I would say 'to map the territory' and 'to map out the territory' imply the same distinction. Hence, in this context, I think 'plot' rather than 'plot out' would be more appropriate. If the distinction is accepted, it would imply that there is a more rational, premeditated, cold, calculating quality to her planning than a passion-driven instinctive non-linear approach.
But I think plot has a negative connotation (e.g. plot an assassination). What exactly was Lady Macbeth planning to do?