Learn Spanish (Latin America): Van a curar lo de la garrapata con la medicina. - They are going to cure the tick thing with the medicine.

The phrase lo de translates loosely to 'the matter of' or 'the thing about'. If the sentence just said Van a curar la garrapata, it would literally mean they are curing the tick itself (making the bug healthy!). By using lo de la garrapata, they mean 'the tick situation' or 'the tick bite'.

Could I use el de or la de instead of lo de here?

No, because you aren't referring back to a specific masculine or feminine noun that was mentioned earlier. The neuter article lo is used because 'the situation' or 'the matter' is an abstract concept or event, not a specific physical object.

Is curar only used for diseases, or can it be used for things like bites or wounds?

Curar is used very broadly in Spanish. While it means 'to cure' an illness, it is also the standard verb for treating, healing, or dressing a physical wound, a bite, or an infection. In this context, they are treating the bite left by the tick.

Why is it con la medicina instead of just con medicina?

While English often drops the article and says 'with medicine' in a general sense, Spanish frequently uses the definite article (la) for general substances and concepts. Alternatively, in this specific context, adding la implies they are talking about a specific medicine or prescription that the speaker and listener both already know about.