When people talk about "Zone 2" they generally do not refer to a specific % of max heart rate. The simple answer is at this volume of training (3-4 times a week 30 minutes) don't even worry about it. Just run. Zone 2 is an optimization. Can you talk while running at this pace? Can you hold a conversation? I think it's unlikely you can over-train at this volume though if you've never run maybe you ease into this over a couple of months.
Adding distance/time into your program is probably going to help, as long as you don't feel too tired/sore or that you're over-training
Consider adding interval training to your regime. That's a more time efficient way of improving your VO2MAX (which should translate to your overall performance). E.g. 1-2 minutes 90%-100%, 1-2 minutes walk/slow/jog, x3-5 (this is rough, do some reading and see what works for you).
So, I thought this might be the case. But I never got a good answer on if power zone or heart rate zone was what to pay attention to. Since I'm not competing and don't plan to, I don't really care that much. But, no reason not to try and train a bit more properly. :D
When biking, it really doesn't help that I have some silly hills surrounding the house. Even if I'm not going all out, a 10% climb takes its toll.
My ex lost 80 pounds and went from unable to run to running ultras and she found that she had to alternate between walking and running in the beginning to keep her heart rate in the lower thresholds. On the converse side, maybe integrating some strength training or speed workouts or stair climbs will help you develop a strength reservoir to make it easier to run at a low heart rate.
Now that you've recognized how gentle a low heartrate feels I'm sure a conversational pace is totally adequate for staying under your lactic threshold (but if you could sing you're going too slow!)
Kudos on that progress! I don't see myself moving to marathons anytime soon. I /think/ I could do a 5k in about 30 minutes. I would be zone 4 in heart rate for dang sure, though. :D
Supposedly this is the definition: "Zone 2 is defined as the highest metabolic output/work that you can sustain while keeping your lactate level below two millimole per liter.". Unless you can measure lactate level you just don't know what heart rate this corresponds to. The heuristic that's used is "able to have a conversation".
For a beginner a good tip is just to go a little bit easier than they think they should be going. Once you've built some sort of aerobic base your training should start including intervals and runs that push you harder.
There are two risks in pushing yourself too hard. Injury and over-training.
There should be some correlation between lactic acid levels and feeling sore. I honestly just don't worry about it. Just getting out there and doing something is better than sitting around. Listen to your body. If you're not recovering, or not sleeping properly or are too sore, dial back a little on either volume or intensity. My Garmin gives me an estimate of recovery time, you really have to work hard to stretch that recovery time into more than 48 hours (e.g. running a 10K race). You can vary your workouts between something that feels extremely easy to pushing yourself a little more.
EDIT: another thing I didn't mention is that in terms of injury you want to give your body plenty of time to build more distance. Most of your joints and other tissues take longer to adapt than cardiovascular. I think this is where people can get into potential injury situations by ramping up too fast. I personally also try to run on soft surfaces (trails etc.) since I find hard surfaces (roads) a lot more punishing.
Adding distance/time into your program is probably going to help, as long as you don't feel too tired/sore or that you're over-training
Consider adding interval training to your regime. That's a more time efficient way of improving your VO2MAX (which should translate to your overall performance). E.g. 1-2 minutes 90%-100%, 1-2 minutes walk/slow/jog, x3-5 (this is rough, do some reading and see what works for you).