In VOY Homestead, Voyager has detected Talaxian life signs 4.9 lightyears away. In VOY Workforce, Kim finds life signs that are 'less than 3 days away at maximum warp', which for Voyager would probably mean 25 light years (source)
That struck me as being very far away. Their sensors would need to be extremely powerful, even accounting for the incorporated Borg technology.
But have we seen larger distances at which a Starfleet vessel has detected life signs (in canon)?
In general, there is not an established distance at which the arbitrary term 'life signs' can be detected.
Indeed, given that it seems to be a colloquial term (I doubt they have a graph on their sensor readout stating 'life signs') that is based upon the interpretation of the person reading the sensors, different people could detect 'life signs' at very different ranges.
Voyager suffers from this wild difference more than most ships would, given that the crew is a mix of Starfleet, Maquais, and random aliens picked up along the way. Once they start heavily incorporating alien technology into the ship, it becomes an even bigger gray area.
It's entirely possible that someone who is monitoring passive sensors and detects regular subspace communications from a location (which could also be referred to colloquially as 'a signal') could report it as 'life signs', as it would be potential signs of life. The same could be said for lightspeed communications such as radio, or an analysis of a planet's atmosphere's chemical makeup.
There are numerous ways to detect signs of life, and Star Trek's sensors (which do have FTL capability when used actively) can likely report on all of them. When close enough (and no, I do not have a definitive answer for 'how close') they can likely detect life signs in a number of ways including heat signatures, bio-electrical signatures, optical sensors (coupled with effective computerized visual recognition), or even remote chemical analysis of the atmosphere around a being.
Out-of-Universe, of course, the answer is "They can detect them at the range the plot requires." Voyager was especially bad about this, possibly due to a more lax adherence to a strict technical manual/series bible or the necessities of creating engaging episodes when the show format practically required 'problem of the week' episodes instead of longer overarching narratives.
