The AirPort may not do the job you need. At the very least it will be lots of work, since you'll need to setup a new WLAN and individually move bulbs to it.
The underlying problem is the number of MAC slots in the network switch part of your current WiFi AP (this is not a limit of the radio, which is limited only by collisions). Unfortunately, device manufacturers do not generally publish the number of slots in their gear, typically called "maximum simultaneous clients". Most generic b/g APs typically support no more than 16 simultaneous clients.
Let's look at the options for getting more slots that do NOT involve setting up a new WLAN.
A. Enable SoftAP on one or more stationary PCs in your home. ($0)
This is FREE if the system supports it. I know Linux and Windows7+ do, but I haven't seen anything about Apple support for SoftAP (but I didn't look too hard, since I have no Apple gear).
Well, OK, technically it is a new WLAN. But at least the gear is free!
B. Get an inexpensive WiFi range extender. ($20-$70)
When using a network range extender (sometimes called a "repeater"), your access point sees only the MAC address of the range extender, and not those of the nodes connected to it. This is kind of like hanging a USB hub off of another USB hub: The PC still has only a single USB "slot" used, but can access more USB devices, and ones further away.
Unfortunately, dual-band range extenders often cost as much a a dual-band AP. However, you need only 2.4 GHz support for Lifx bulbs.
Update: Just found this tiny versatile repeater for $15!
C. Replace your current access point with one that has more slots. ($100+)
By getting a better AP, you can reuse the network configuration, and not have to reconfigure any clients.
In general, a MIMO AP will have a full set of slots available per antenna, since each antenna connects to a separate WiFi radio. So, as a general rule, more antennas means more simultaneous clients. Be sure that "MIMO" is in the product spec, and not just "diversity" (which merely selects between different antennas for a single radio).
Most MIMO APs have 4 antennas. There are some dual-band APs that have 8 antennas (separate antennas for 2.4 GHz and 5 GHz, instead of using dual-band antennas).
CAUTION: Some MIMO APs have internal antennas. Check the specifications to be sure how many there are.
MIMO is a complex beast, since when talking to another MIMO device it can simultaneously use multiple antennas AND multiple frequencies AND "beam steering" to get awesome bandwidth boosts (802.11ac).
But the Lifx bulbs are b/g only, and so can't take advantage of such MIMO benefits. But MIMO APs are OK with this, and can act a 4 separate b/g WiFi radios combined in a single AP.
Also, since the Lifx bulbs use only 2.4 GHz, getting a dual-band AP could be overkill, but it may be helpful to move your high-bandwidth devices to 5 GHz.
If you do replace your current AP, check to see if it supports a "range extender" or "repeater" mode. If it does, then put it into that mode and gain the best of both worlds.
Finally, there may be some good reasons to put all home automation devices on their own WLAN(s):
Access Control: If folks share your WLAN, they also gain access to your bulbs. Best to have HA on one WLAN, residents on a second, and guests on a third WLAN,
Cost: HA is low bandwidth (other than video), and few HA devices support 5 GHz. So put HA on less expensive 2.4-only equipment.
Reliability: If an AP goes down, you don't lose everything, just that single WLAN.
I'm still working my way through all of this. In general, WiFi is not a good medium for HA (too "heavy"), but is being used mainly because WiFi is the only wireless support available on consumer devices. My long-term plan is for all my HA devices to be 6LowPAN, but I can't make the switch until 6LowPAN support is built into more consumer devices (PCs, tablets, phones). So I'm using WiFi for the moment, which means finding work-arounds for WiFi's limitations when used for HA.
There are strong arguments to have the most vital HA nodes on wired Ethernet, and not on any WLAN.
Here's some of how my thinking is going: Since my "Super Nodes" use Raspberry PIs and will be powered via PoE, why not add a PoE AP? The Intellinet 300N is ceiling-mounted, getting it above most obstructions, and thus increasing its range. It would be PERFECT it it also contained CO and Smoke detectors!