A couple of months ago, an early build of Ice Cream Sandwich showed up for the LG Spectrum, yet we haven't heard a peep since then, until today. Apparently an LG employee shared that Android 4.0 might not be too far off. Here's a quote with the details,

An LG representative has spilled the beans on the incoming ICS update for the LG Spectrum. According to hints on the phone’s support forum, the ICS update is apparently “getting very close.” He falls short on giving a timeline and leaves the task of setting a OTA schedule to Verizon.
Source: AndroidAuthority