In this video George turned on his Sylvania SHP-TS mercury free HPS lamp. However, the lamp cycles in this video, despite it don't have mercury.
Can really mercury free HPS lamp cycle at EOL? Or what can cause mercury free HPS lamp to cycle?

@James?

@James, @RRK, someone?

Normally not so soon as a regular HPS lamp.  But if they live long enough for the arc tube to become severely blackened and raise the sodium vapour pressure and lamp voltage, I cannot exclude that it might be possible.  Especially if combined with dips in the mains voltage.

But the sodium is lost from the arctube as the lamp age. This is the cause of regular HPS lamps to become redder during life. Not?

There are two mechanisms at play: Arctube blackening (leads to cycling by itself) and sodium loss (does not lead to cycling by itself). Depends which is faster, so dominant at certain point of age, the lamp will or will not become a cycler before it gets replaced.

It is the presence of mercury that generates the redder light in an HPS (or metal halide lamp).  Of course not from spectral radiation of the mercury itself, but increased mercury pressure influences the spectrum of sodium such that it becomes broader (similar to how raising the sodium vapour pressure alone broadens its spectrum).  However, the influence of mercury is not symmetric - it only broadens the spectrum on one side towards the red wavelengths.  It also causes a sharp rise in lamp voltage.

Since mercury is not lost from an HPS lamp during life, the % mercury : sodium ratio rises so the relative mercury vapour pressure rises during life (due to sodium decreasing).  Moreover as the arc tube blackens it traps more heat which amplifies the relative increase of mercury vapour pressure.  This is the mechanism by which standard HPS lamps become redder during life.

With Hg-free HPS that cannot happen of course.  But there is also an interaction with Xenon.  In the plasma, sodium-xenon quasi-molecules are formed and their radiation is principally in a narrow green band which you can see on the short wavelength wing of any HPS spectrum containing Xenon.  It is somewhat more significant with Hg-free lamps only because there is no red-broadening due to presence of mercury.  As pure Na:Xe lamps age, there is of course a relative shift in the Na:Xe pressures and this also has electrical and spectral influences, but far less than with mercury.