The formula stored for this lot is Ascendant plus 19 degrees of Aries minus the Sun. Nineteen Aries is the exaltation degree of the Sun in the classical scheme, and it is a fixed point, not a body. No other lot in this atlas has a term that does not move.
That produces a property none of the others share. Change the zodiacal reference frame, from tropical to sidereal or between one ayanamsha and another, and every planetary longitude and the Ascendant shift by the same amount. In a lot of the ordinary form, Ascendant plus one body minus another, the two positive terms each gain the shift and the negative term loses it, so the lot shifts with everything else and its position relative to the chart is unchanged. Here the fixed 19 Aries does not shift, so the shift on the Ascendant and the shift on the Sun cancel and the lot stays where it was. Relative to the rest of the chart, the Lot of Exaltation moves when the zodiac is changed and the others do not.
Its motion in time is otherwise unremarkable: the Ascendant's full circle less the Sun's 59 minutes a day, so about one degree every four minutes and one sign in two hours.
Anyone comparing an Exaltation lot cast in a tropical chart with one cast in a sidereal chart is comparing two different points, and the difference is the ayanamsha itself, currently around 24 degrees.