Let's take a hypothetical example of a person who is not extremely depressed and doesn't live in especially awful conditions, but is often accompanied by thoughts that life is not worth living. Then, let's say the person in question honestly wants to change his outlook on life, i.e. he wants to increase his will to live. Do you think attaining stream entry would help him in this regard - 1) almost definitely, 2) likely, but only to a certain extent, 3) probably not.

To clarify, I am NOT intending to commit suicide! (Certainly not while my daughter is still a child, so next ~15 years are off the table.)

 I'm truly sorry you feel  that way. Stream entry is a marker of the wisdom that comes from realizing certain aspects of the nature of experience. It can certainly have an effect on our outlook on life, but there's no a guarantee. Have you explored therapy as another way to address the issue?

Rather than considering it in a goal-oriented way, I suggest focusing on process. Why not commit to some process that strengthens wholesome factors and weakens unwholesome factors? One way is TWIM, which is basically about bringing back metta and weakening all the craving that pulls your attention away from it. I'm sure you have heard before, it's somewhat paradoxically better for the goal to attend to the process that makes the goal happen rather than thinking too much about the goal itself.

My opinion is that awakening, all 4 paths, lead to an increased intimacy with experience and a decreased driven-ness/compulsion to change it.

One way of framing it is to say that the heart is pulled out of concepts, thereby concepts lose their 'oomph'.

Life is fuckin wondeeful man! - all oomph is sucked out.

Life sucks man! - all oomph is sucked out.

What is left is the ability to have wholesome positive agendas and the gumption to act on them. This ability has to be utilized thereby we get good at it.

I hope my answer helps. I wish you happiness and joy.

Feeling that life is not worth living is a sign of depression.

Whether meditation would help depends on a lot of factors. Primarily I think it would depend on whether the cause of those feelings is cognitive or organic. If you are depressed because of cognitive distortions, then meditation could help a lot. If the cause of those feelings is due to mostly biological factors then meditation might not help as much.

My opinion is, if you are already meditating regularly and you have those feelings, stream entry probably won't help much.

I'm basing my opinion on probabilities and reading an internet post and there could be exceptions to my generalizations for many reasons. So in your particular case my reasoning might or might not really apply.

My advice would be to look at your diet and see if that could be the problem. There is a lot of information on the internet about how diet affects mood. Everyone is different so don't take any one source a gospel and try things for yourself. (I am pretty sure that there are many people taking medication for mood disorders who wouldn't need it if they got their diet right - I am not suggesting anyone reading this go off their meds.)

Also, different types of meditation affect people differently, have you tried stopping meditation or trying a different type? That might help too.

Another thing to consider is if you have felt this way all your life or not? If it is recent, is there some factor in your life that changed recently that might be causing it?

The gentlest form of meditation and mindfulness in daily life I know of is just being aware of what you are experiencing in the present moment, what you are seeing, hearing, feeling, etc - without intense effort to concentrate just gentle awareness - without your mind wandering into the past or future or problem solving etc.

This might be helpful too:
https://palousemindfulness.com

Most of all sending you much love and best of wishes! 
Hang in there! That too shall pass! 

In my experience with combat PTSD which also has much to do with being abandoned by my parents at an early age and living with several foster families, stuff can subside but also return casting agony and depression. 

Before SE there was this Me really suffering. After SE the me lost its position behind the eyes and "I" was nowhere to be found. 
However reactive patterns were still arising/unfolding and causing suffering. 

That's the road to 2nd Path for me. Seeing that all my suffering is made of these reactive patterns and really clinging does lead to suffering (2nd noble truth). 
Here I felt as if there is no point to all this unfolding mess of a life/experience. What can I do about all this??? I'm too tiny to handle this?!! It's too much! 

Here I felt life is utterly pointless. I didn't mind dying but I haven't had suicidal tendencies. Just a wish to pari-cease to exist in the Buddhist sense. But how?  

So after 2nd Oath now it's time to re-learn the whole meditation! Total beginner again!  

So what do I have now: 
1. no locates witness behind the eyes
2. reactive patterns running the entire show without me in it as a deciding factor. 
3. seeing that believing in my own suffering and insisting it exists I kind of drag it through time. It lasts. Or there is a sense that it lasts. But does it last? Hm ... I'm here now trying to figure out the road to 3rd Path which is the Nobel 8 Fold Path. 
The whole feeling tone at this stage is kind of shit-sweet. Like chewing on shit and honey at the same time. 

Im not sure what I'm trying to covey here to you but stuff seems to be the same in our life. As Chris once told me "it's not about what we are experiencing, buu how we look at it". That's what is changing with the 1st Path then 2nd path then 3rd then ... what know I  

​​​​​​​Ok I will shut it now! Sending best wishes! 

Oh and just to add; I just recently went back to SSRI meds again as my family situation got out of hand and I just couldn't handle it calmly. Meds are helping a bit but so is so ailing at work and playing badminton with my team once a week. Therapy could do well for me but have no time nor money for ut right now. 

Stream Entry is not about will to live but being aware you need to protect your mind.

You say he wants to increase his will to live and I read he want's to experience relief - exactly the sheet mind needs to be protected from.

I do not mean any specific convoluted meaning of term "relief" but all of it - every single thing in which you think it is good experience is the lie you told yourself long time ago and just went with it assuming it is the only way.

When you are e.g.. outside on hot day outside and enter air-conditioned room, the pleasure of relief you indulge in is what you need to protect your mind from. So do not call what you need to protect mind from as only "desires" or "clinging', etc. also do not call it "sensual pleasure" - it all has nothing to do with pleasure of senses. The aspect of it which causes issues is exactly the experience of relief - it actually removes pleasure from both hot and cold in this case.

Nibbana,
Ni

In all honesty, I think you'd be better off talking to a proper professional (physician, psychiatrist, psychotherapist) rather than random folks like us. From what I've read, good sleep, good nutrition, and vigorous physical exercise are the best home remedies. MBSR and MBCT also have some research in their favor.