We have to look through the thick cloud of fuzzyness to find the relationship, if any.
According to IDEO, Design Thinking is a "human-centered, design-based approach to helping organizations... grow... identify new ways to serve and support people by uncovering latent needs, behaviors, and desires."
On the other hand, "Business Architecture" today is not really about architecture, as in the blueprint of an enterprise, but about business processes, their improvement, requirements management..., that is about BPM practices. But business analysts are newly called now business architects. Just check a few roles descriptions, if not sure.
The term "business architecture" was adopted by the business analysts' community under pressure from enterprise architecture. It does not have the same meaning as it has in EA, as a layer in the overall enterprise architecture.
At first sight, Design Thinking sounds like applying scientific "design" principles (thinking) to organization development, if I were to use the logic of words.
That may sound like Enterprise or Business Architecture to many. Still, Design Thinking is not really about EA because the "design", in practice, is applied for the enhancement of business flows and human interfaces rather than for the modeling of the enterprise blueprint.
In fact, the "design" paradigm was not really adopted from technology but rather from art, or say, industrial design, because the Design Thinking does not mean design methods like IDEF, BPML... but design methods aimed to round the human experience.
Design Thinking complements "Business Architecture (BPM) by forming together the Business Process Design discipline that takes into consideration in process modelling human "latent needs, behaviors, and desires".
In terms of EA, business processes designed for people would enhance the enterprise operation. But business process re-design as such is not really the object of EA, but in itself it is a business goal that determines the target EA.