"Je dois changer de lentilles de contact."
Translation:I need to change my contact lenses.
There are some difference:
To be concise :
"devoir + infinitif" = obligation or high need
"falloir + infinitif" or "falloir que + subjonctif" = obligation or high need
"avoir besoin de" = need
Here "Je dois changer de lentilles de contact" it's not an obligation, it's not a duty or nobody force me to change them. It's a need, an important need but a need and there is no obligation to do that so "I need" is the best translation.