Which Sonalert device were you considering? Would need to know its specs to have a good idea which SSR would be most optimal. Assuming it draws less than 500mA, here’s a short list of options to consider.
Also, devices that turn on LEDs are sometimes a bit tricky, as LEDs are current-controlled rather than voltage-controlled. This means that tapping into that signal may have unintended consequences to the LED drive circuit (reduced brightness, or possibly even not operating at all). If you measure 2.7V across the output when the LED is lit, and it is drawing more than 50mA, then putting an SSR in parallel, with proper current limiting (preferably drawing no more than 10% of the LED’s current) is not likely to significantly affect the rest of the circuit.
The typical SSR capable of being triggered by 2.7V or less uses an internal infrared (IR) LED to trigger an IR sensing MOSFET on the output side. The input IR LED needs to have a current-limiting resistor to prevent over-current of that LED, as shown here:
To select the right resistor value, you need to know the input voltage of your system (presumably 2.7V, from what you state), the forward voltage drop of the SSR’s IR LED, and the required current to properly trigger that IR LED. This info can be found in the respective SSRs’ datasheets.
Once you know these, you can calculate the proper current-limiting resistor value by figuring out the required voltage across it and the current to be passed through it. The voltage across the resistor can be calculated by subtracting the IR LED forward voltage from your input voltage (presumably 2.7V in this case). Since the resistor will be in series with the IR LED, the current passing through the resistor will be the same as that passing through the IR LED.
Then using Ohm’s Law, since resistance can be calculated by dividing the voltage across the resistor by the current passing through it, you get the following equation:
Rcurrent limiting resistor = (Vinput - VIRLED) / IIR LED current
Since the current passing through the IR LED is typically set to 10mA or less, the power rating of the resistor is typically not a worry. Therefore, 1/4 Watt or 1/8 Watt should suffice.