Look into installing a multi-stage filter that you can set up beneath your kitchen sink. You can set up a charcoal, sand and reverse-osmosis (RO) filter that will remove most contaminants.
You can even buy a "filter" that will remineralise your water for you - as the filters will remove everything, even the good stuff - but I would just rely on good quality food to fulfil that role, personally.
An example, available in the UK, is
https://www.finest-filters.co.uk/50gpd-4-stage-complete-ro-reverse-osmosis-unit/
If your water is likely to contain bacteria or viruses, you'll want an inline UV filter too.
I'm not certain that the above will remove all of the lead but it will certainly help with chlorine levels (the pool smell) and it
should remove dissolved solids and at least some of the heavy metals.
You will have to replace the charcoal filter semi-regularly (they are cheap) and rinse the mesh/resin one (read instructions for a specific set up).