I don't see how you can do much better than hPutBuilder h b = L.hPutStr h $ toLazyText b because Builder has to construct a list of chunks anyway (as you mentioned yourself in the linked issue).

The only place I can see a potential speed up is if the desired encoding is UTF-8, then you could go through Text.Utf8.hPutStr, whose implementation could be improved by removing the encodeUtf8 copy and writing the Text bytes directly to the handle.

text's Builder's only purpose is to produce a LazyText, so I think it makes sense to keep its current API minimal and not even add hPutBuilder. Note that it's a quite different data structure from bytestring's Builder, which doesn't allocate buffers itself. Converting Text to bytestring's Builder may be a better idea than going through text's Builder.