You can just google for "taxi lörrach". Most companies can be only reached by calling.
Here one you can mail to
and this one has an online form
From Basel Airport to Lörrach you have to expect around EUR 40. For this trip you can negotiate the price.
For trips inside the district (county) Lörrach the official taxi tariff is binding, taxi meters must be used.
A day ticket public transport covering Basel Airport to Lörrach is EUR 9,10 (triregio mini).
Lörrach public transport network map (PDF)
Thanks for helpful replies. Is it worthwhile pre-booking beforehand - pricewise? since we will be arriving from airport so there might be delays
I don't think there's a price difference. I would just take a cab at the taxi stand.