Salam Hilary,
Actually in the Jordanian accent, both هيك and زي هيك give the same meaning, which is: "like that: مثل هذا". I usually use "هيك", but you really can use both if you like. Examples:
1. طعم الأكل زمان كان زي هيك/ هيك: The taste of food in the past was like that.
2. ارمي الكرة زي هيك/ هيك: Throw the ball like that.
Yet the word هيك has more meanings than just "like that", let me give you an example:
1. هيك: "this is how", like in:
هيك خبّروني: this is what they told me.
In this case you only use "هيك".
2. لهيك: the letter lam is added here because هيك here is used to "give a reason why", like in:
السوق كان أزمة، لهيك تأخرت: The market was crowded, this is why I was late.
أنا تعبانة، لهيك رح أنام بكير: I'm tired, this is why I want to sleep early.
Only لهيك works to give this meaning.
If my examples weren't clear, do tell me Hilary :) I wrote them in my Jordanian accent to increase your vocabulary, and because هيك and زي هيك are only used in the spoken accents, but we never use them in MSA. I wish you good luck.