I know this answer has already been given, but giving some different and hopefully more complete reasoning here.
To the lonely I call (the title)
People often suicide by drowning themselves and/or jumping off bridges into water.
I climb only to fall,
The water cycle; evaporating into the clouds, only to fall as rain - and continue falling by running downhill.
and people often avoid me.
People generally avoid puddles, avoid going out in rain, and go around lakes and ponds or over rivers and streams - not through them.
They may not care at all,
but they all know that they need me.
Many people aren't particularly concerned about their water intake, but we all know we need water to live.
I can fill the streets and invade your house,
Flooding does these, of course.
but most of the time I fall under.
Typically, rainwater falls under streets through storm drains, and wastewater falls underground and under streets through sewer systems; fresh water comes to our homes etc. through underground pipes, and more generally, natural water is below ground in aquifers.
Leave you feeling unaroused,
and even make you wonder.
Those last two, which I don't think anyone alluded to, inspired this answer.