There is something you need to consider before you make a decision:
Power vs. Beam quality-
The high power lenses are single element aspherics. They collect the most light from the diode and losses are small. While the power is ~25% greater than with a 3 element Aixiz lens, the beam profile is much more elongated. The beam diameter at the aperture will be much smaller (~0.7x4mm) but this means that divergence will be larger (beam diameter and divergence are inversely related).
The Aixiz 445nm lenses use 3 elements. This causes more loss in the optics. Also, the numerical aperture is not as large. Some of the beam gets "cut off." The beam diameter at the aperture is much larger (~4x5mm) but the divergence angle is smaller. This lens forfeits much of the power for a more "acceptable" beam overall.
If your only concern is close range burning, go with the high power lens.
If you want a beam that is ok for pointing and long distances, stick with the Aixiz 445.
Due to the nature of these diodes, collimating the light is difficult without optics designed for beam correction.
The beam characteristics of single-mode diodes with the high power lenses is much better than with these multi-mode 445nm diodes.
You can get the high power lenses from 2 sources. They are actually coated for ~405nm but transmission at 445nm is still very, very good.
LarryDFW sells them in a custom brass mount with tighter thread tolerances.
Jayrob sells them in a modified Aixiz mount.
From either seller they cost about $60.