I think it's ambiguous because their can refer to both the Lakers' and the Lakers' coaches. Is there any hard-and-fast rule on this?

The use of smart clothes helped the Lakers’ coaches improve their training program.

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There is presumably one training program that is run by the coaches and used by the team. The word "their" might refer to either the coaches or the team,and so could be called ambigious. But it is, after all, the same program in either case, so any ambiguity is trivial and inconsequential.

Moreover since "the Lakers’ coaches" is the noun phrase they comes most closely before "their" the normal conclusion is that that NP is the antecedent of "their". Thus there is a further reason not to consider this sentence ambiguous. There is certainly no confusion of meaning here.

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