When you’re refinancing and your LVR is above 80%, then you might have to pay LMI again i.e. if you have less than 20% equity in your property, then you might have to pay LMI.
To avoid this, try to pay down as much of your loan as possible so your LVR is 80% and below.
If you’re refinancing to add a partner, then you might be able to avoid paying LMI if your partner can share the cost.