The AP-124 uses (female) RP-SMA connectors, while the AP-LAR-1 connects to a (female) N-type connector. The AP-ANT-9 antenna has a (male) RP-SMA connector, and can attach directly to the AP-124, but if you want to use the surge arrestor in between, you'll need several adapters.
First, are you sure a lightning surge arrestor is needed? Unless the antennas are exposed and/or you're installing them in an area where lightning is common, you may not need these. If you do need to use arrestors with this AP and antenna, you may be better off looking for an RP-SMA style arrestor. Aruba doesn't offer these, but they can be found elsewhere.
Also, why are you using AP-ANT-9 with the 3x3 MIMO AP-124? AP-ANT-17 or -18 are a much better fit when sector coverage is needed with this AP model. You'll need just one of these antennas per AP (they integrate 3 antenna elements for 3x3 operation), while you would need 3x AP-ANT-9 per AP.
Finally, if 120 degree sector coverage is ok (AP-ANT-9 is 90 degrees), you could consider using AP-ANT-92, which is equivalent to AP-ANT-17, but has N-type connectors, so they can connect directly to the AP-ANT-LAR devices (you'll still need adapters between the AP and arrestor though).