To understand how [the rate of diffusion of technology depends on economic interactions—on trade—], and thus to understand the extreme variability of development experience and the policies that lead to successful development, we need to get deeper into the nature of knowledge spillovers (Lectures on Economic Growth, 9).
Is Lucas simply saying that trading partners inadvertently share more than goods and capital, or is he also saying that free trade causes or deliberately brings about the exchange of know-how? Because we could also say that before ideas can promote productivity in a country with whom we trade, there must be in that country a fairly complex set of institutional arrangements, capital assets, and human capital that make the use of that knowledge, and the sharing of this knowledge, likely and possible.
Here, as elsewhere, correlation need not entail causation and often does not. While we will not pick the nit over whether technological diffusion “depends” on trade, we would also like to point out that it depends on much else besides and that, causally, these other things might be more critical than trade.