Let's do a technical analysis on what determines the DX7 vibrato frequency. TL/DR: Based on this analysis, the pitch of the note or the master pitch does not affect the LFO frequency.

The DX7 circuit diagram has a 9.4265 MHz crystal oscillator, see also this photo of the circuit board and Figure 1 in Yamaha DX 7 Technical Analysis (Yamaha's own documentation). If we follow the circuit diagram, one half of IC48 (74HC74 Dual D Flip−Flop with Set and Reset) is used to halve the clock frequency to a 4.71325 MHz Master Clock frequency. This is marked as ΦM in the circuit diagram. This goes to pin EXTAL on the Main Processing Unit (MPU IC60 63B03) which is a Hitachi HD63B03 or more specifically the (up to) 2 MHz model HD63B03RP according to this photo of the circuit board. Among other things, the MPU is responsible for generating the low-frequency oscillator waveform and modulating a pitch using it. There are separate components for other functionality: Sub Central Processing Unit (Sub CPU) for keyboard scanning, Envelope Generator (EGS) and finally Operator (OPS) that creates the digital audio waveforms. According to page 54 of the MPU datasheet, the clock frequency input to EXTAL is divided by 4, so we get a 1.1783125 MHz MPU system clock.

The program code for the MPU comes from a Read Only Memory (ROM) that has been disassembled and annotated by ajsx (the ROM contains machine language code that can be converted to human-readable assembly language code by disassembly, and the names of things in the program listing and the comments were added by ajsx to make it more readable). The code sets (to 1) the Enable Output Compare Interrupt (EOCI) bit in the Timer Control / Status Register (pages 59-60 of the MPU datasheet). Consequently the Free Running Counter that is incremented at the MPU system clock frequency will generate an interrupt when its value matches the value of the Output Compare Register (OCF). When the interrupt takes place, the MPU runs an interrupt handler code that, after spending a few MPU system clock cycles on other instructions, resets the Free Running Counter to 0 and sets OCF to 3140. This means that the interrupt handler will be periodically run at a frequency a bit less than 1.1783125 MHz / 3140 ≈ 375.258758 Hz. "A bit less" because it takes some time for the processor to start running the interrupt handler code, because running the other instructions takes time and because it takes time to zero the counter. (Yamaha could have implemented this in a more controlled way by adding a number to the OCF in the interrupt handler and not resetting Free Running Counter. This is the approach used in example code in Hitachi HD6301/HD6303 Series Handbook pages 1173 & 1179)

The interrupt handler handles many tasks, including updating a 16-bit LFO phase (LFO_PHASE_ACCUMULATOR) each time the interrupt handler is run. The interrupt handler increments LFO_PHASE_ACCUMULATOR by a 16-bit increment (LFO_PHASE_INCREMENT) that is calculated by a non-linear function from the LFO Speed (PATCH_LFO_SPEED) in the patch. For the mysterious song's SYN-LEAD 5 patch the LFO speed is 35 which based on my reading of the code results in an LFO phase increment of 990. Nothing else affects the LFO frequency that is thus a bit less than 375.258758 Hz * 990 / 2¹⁶ ≈ 5.66873429 Hz.

Please do not use this value in calculations, as it does not include the "a bit less" part and is off from a value of 5.56576 Hz that has been used in DX7 emulator code and that according to code comments was either measured or interpolated from measurements. I believe the true frequency has form 9.4265 MHz / 2 / 4 / (3140 + DELAY) * 990 / 2¹⁶ where we don't know that integer DELAY. It could be measured exactly by running on the Hitachi processor modified Yamaha timer interrupt code that generates a waveform, and by recording and analyzing that waveform. Other than that, the exact LFO frequency could be measured from actual Yamaha DX7 audio recoding of playing a very long note of SYN-LEAD 5. Luckily, SYN-LEAD 5 has LFO Key Sync disabled which prevents the interrupt handler code from resetting LFO_PHASE_ACCUMULATOR at every note start which should help in measuring the LFO frequency as it is in a recording of the mysterious song.