Lakoff (1993) highlights that mapping cannot be thought of as an algorithm that takes source domain inputs and produces target domain outputs. Any justification?
The paper should probably be "The contemporary theory of metaphor" published in Ortony's second edition of Metaphor and Thought (1993). If that is the case, perhaps what motivates the question is the fact that Lakoff's view of metaphor as a mapping was qualified "in the mathematical sense" which makes it "tightly structured" (pp. 206-7). Now, as answer to the question, the mapping is the outcome of two categories, a source and a target, which come to the mapping with their own frames of knowledge. Since the target is structured by the source, the target will only take from the source that which is pragmatically relevant within the topology (i.e. the internal structure) of the source to the target. Lakoff called this regulatory principle in metaphoric mappings as "the Invariance Hypothesis" (1990). If this is what you mean by "fixed pattern of correspondence" in your question, this is it. If the frame within a category is not stable enough to create the mapping, metaphor will not be possible and made sense of. Language change is not an everyday occurrence; it is slow in time. However, the mapping is not immune from cultural interpretations as Lakoff and Johnson (1980, 1999) repeated it constantly.
Metaphorical meaning cannot be explained by projection, but has to refer to the process of conceptual blending. And same imagery gives different output meanings if the schematisation of the blend is different. See "How to make sense of a blend", Brandt and Brandt 2005.