Depends on what type of workout you're doing.. but keep in mind that you're actually getting stronger (ie. building new proteins, neuro adaptations, etc.) when you're resting and sleeping. If you're doing a fully body routine like starting strength, you absolutely need rest days after every workout. Light aerobic activity doesn't interfere with that - training for a marathon or something like HIIT would.
If you're doing something that splits your lifting up into 'arm days' / 'leg days' you can certainly lift more often. Some things (upper back) recover very quickly, while other things take more time (e.g.doing max deadlifts more than about ~1x /wk is asking for injury). Altho I'd recommend that if you're doing a split, you should stop doing it and start doing something like 5x5 Stronglifts / Starting Strength / etc.