Why does MATLAB's dualtree3 function not return the lowpass subband of the imaginary tree?
Prof. Nick Kingsbury kindly provide an answer to my question!.

In 1-D, the lowpass basis functions (scaling functions) from the two
trees (a) and (b) of the dual tree WT tend to look very similar to
each other, apart from a shift of half the output sample period
between them. Hence it usually makes most sense to regard the two sets
of lowpass samples as interleaved samples from a single 2x
over-sampled real basis function.
On the other hand, the highpass basis functions (wavelets) from (a)
and (b) look approximately like a Hilbert pair of functions. so they
are most logically interpreted as the real and imaginary parts of an
analytic basis function.
Hence the over-sampling by 2 in the lowpass channel replaces the
spitting into real + imaginary channels for the bandpass channels of a
multi-scale wavelet transform.  Similar things apply when 4 trees are
used for the 2-D dual-tree WT, or when 8 trees are used for the 3-D
version.
I hope this helps.  Do refer to our 2005 paper in IEEE Signal
Processing Magazine for more details.

[UPDATE at 9/18/2020]
Since I quoted Prof. Kingsubury's answer above, I should also note one more thing. He mentioned in his email that he is not familiar with dualtree3 function in MATLAB. However, based on my question, he gave the above general answer.