simulate this circuit – Schematic created using CircuitLab
A problem (of sorts) is that the AC supply is notionally isolated from the logic supply - see diagram below - BUT if it is the same supply as on page 14 this is not a problem. . Two mains choices to get dimming information are
IC33 is an optocoupler. By using an identical or similar optocoupler with input connected from +5V to MOC_EN via a suitable resistor. I cannot see where MOVC_EN is derived from but it will probably allow a second opto to be used - one with more sensitivity and a larger resistor would help minimise extra load.
The dimmer shows a 24 VAC signal on page 14, used to supply power via a bridge rectifier to the logic circuitry. If this is the same as the one used for the map in the circuit below then this output can be used as a dimming voltage source.
Using AC lamp output for dimming signal source:
Connect a single diode (Dl)from (or a bridge rectifier for less ripple) from lamp output to a resistor (Rl) to ground. Add a "suitable" capacitor (Cl) across Rl. Rl should be as large as works OK. ie a resistor giving full lap load will replicate the lamp voltage but dissipate as much power as the map. Probably a 100 Ohm to 1k resistor will work. 1k to 10k may. 10k is best if it works. Size wattage to suit. Cl filters this to a DC level. Using a bridge rectifier (see page 14 BR1 as an example) will provide a smoother DC signal. Extra filtering may well be needed - this can be discussed if this answer looks useful. System gain control or an external potentiometer (or both) will control relative brightness.
On off control can be provided by detecting a minimum DC level for LED turn-on (as you suggested).
Try this - see text below and in comments
However - an "easy" possible solution (depends on LED power voltage) would be to power the LEDs directly from the existing output using the existing AC rectified with a bridge rectifier. I assume the LEDs use 12VDC for main powering - maybe not. If V_LED_power is >> 30V then the following does not work.
LEDs would either need to accept up to 24 VDC or the system arranged to "not overdo it". A one resistor addition to the optocoupler drive would allow lower maximum output voltage levels. As the original unit can drive 250W at 24 VAC, driving a 12VDC 80W load would work.