While there have been many reports of them blocking X10, I do not recall any reports of noisy CFLs causing random ONs similar to these. However, noise of significant amplitude may act in the same manner as spikes (see below). Are the three lights in question CFLs?
It is difficult to offer meaningful suggestions without adequate information. The presence of CFLs was not known before and we still have no clue as to what switches or modules are in use. The stick-a-switch sends radio signals to the PAT01 which then sends powerline signals to whatever switches or modules actually control the three lights.
Normally, it takes about 100ms for the radio signal and about 400mS for an Address plus ON or OFF signal from the PAT01. If you were experiencing longer delays it could be due to...
1. a weaker radio signal. The switch sends 5-6 copies of the signal and the PAT01 has AGC which can respond to a weaker signal, perhaps needing 2-3 copies before it can discern a valid signal. X10 RF signals from these switches are problematic to begin with and are easily disturbed by changes in the environment.
2. powerline noise causing the PAT01 to delay its transmission.
Random events are usually caused by spikes or brownouts. Spikes can come from motors, old-style magnetic fluorescent ballasts, and some smartmeters. Brownouts are brief voltage dips that cause the microcontrollers in the switches/modules to reset which almost always results in them turning on when off.
It is highly unlikely that the stick-a-switch or PAT01 are involved in the random ONs. The likely culprits are whatever switches or modules actually control these lights being acted on by spikes or brownouts. Since you mention the neighbors have a vacation home, I would look into whether your electric utility may be allowing power to dip a bit in the middle of the night.