I cannot guarantee that this is the best solution but I am able to make it
work this way if the tables are "full width", i.e. from left to right margin:

1. Set the preferred table width to 100 % (Table > Table Properties > Table
tab > Preferred width). Make sure "Automatically resize to fit contents" is
_turned off_ ( (Table > Table Properties > Table tab > Options).

2. For each column, set the preferred width to a measure in _percent_ and
make sure that the sum of the column widths makes up exactly 100 % (e.g.
column 1 = 20 %, column 2 = 30%, column 3 = 50 % in a 3-column table).

This way, if you change the page orientation, change margins or change the
paper size, your tables will automatically adjust to fit from the left margin
to the right margin and the column widths will be distributed proportionally
to their original widths.

Note that if you need indented tables (i.e. tables that are not full width),
it is more complicated because the indent is a fixed size. Therefore, even if
you can calculate which preferred width percentage to use for e.g. A4, that
percentage would no longer be correct if you change to Letter.