I found some things, but with your content and coding which I appears to be most of the cause of your issues in ie8. I realized that I actually did make Preference Lite almost 100% compatible in ie8.
First thing I found:
In your child theme style.css, you have this:
Problem is that first part needs the ID part like this:
Plus....you need a closing curly bracket for it as well, even though there is no style attributes there.
Second thing is with your front page image boxes (in the widgets), which I will post just the content from the text widget only.
<p><a href="http://www.westendtablecraft.com.au/benches"><img src="http://www.westendtablecraft.com.au/wp-content/themes/preference-lite-child/images/bench-set.jpg" width="265" height="180" alt="Quality wooden bench sets" class="imageborder" style="display: block; margin-left: auto; margin-right: auto;"</p><p>Quality wooden picnic table and bench designs designed to suit any outdoor area!</p>
Your <img> tag has no closing: />
Third thing is...you made some modifications for the main menu which are causing some minor layout issues in mobile view. Also make sure that you make a custom menu and not the default "page" menu WP does; a custom menu is what the theme is styled for.
The fourth thing is... did you copy your content from another source? I noticed a ton of inline styling throughout your page content. This could have some influence on how the pages and site looks. If you did copy from another source, copying also copies inline styling of elements such as this one line from a page:
<p style="margin: 0px 0px 1.25rem; padding: 0px; border: 0px; vertical-align: baseline; color: rgb(40, 40, 40); font-family: 'PT Sans', Arial, Helvetica, sans-serif; font-size: 13px; line-height: 21px; background-color: rgb(248, 248, 248);">
....way too much css in your content code.
Now for my end... ie8 is ignoring a script that is supposed to help ie8 understand HTML 5 elements, but it's ignoring them. So I have to figure this one out as the same script works for my other themes.
I will be uploading this update for Preference Lite today, but you can contact me from my website Contact Me to get a new copy right away.