I wouldn't classify myself as an LED guru, but the datasheets from Lumileds imply you might not be much better off. For the sake of simplicity, let's assume that the Fenix drives the emitter at its claimed current of 350mA.
Here's the datasheet for the LuxIII (pdf file):
http://www.lumileds.com/pdfs/DS45.PDF
Figure 6 at the top of page 12 indicates that the normalized luminous flux at 350mA is going to be about 60% of the flux at the specified current of 700mA.
Table 1 on the top of page 3 indicates that the typical luminous flux at 700mA is 65 lumens for a white emitter.
So you can guesstimate about 65 x 0.6 = 39 lumens.
Note that Lumileds cautions: "Driving these high power devices at currents less than the test conditions may produce unpredictable results and may be subject to variation in performance. Pulse width modulation (PWM) is recommended for dimming effects."
The datasheet for the LuxI (pdf file):
http://www.lumileds.com/pdfs/DS25.PDF
Table 1 at the top of page 4 indicates that the typical luminous flux for a white LuxI driven at 350mA should be 45 lumens.
Of course, YMMV. The figures quoted above assume that the LuxIII's Vf at 700mA is 3.7V (which would classify it as a K bin), and the LuxI's Vf at 350mA is 3.42V (J bin). So if your Fenix happens to have a LuxI with a high Vf (R3J or R3K), you might see some improvement after transplanting your TWOH.
You also might want to keep an eye on this thread, containing pbarette's experiments with a Fenix circuit with a R/O Lux3 (of unknown bin) and a QYAJ Lux 1:
http://candlepowerforums.com/vb/showthread.php?t=99516