Welcome to the forum, beepherd!
It’s a tricky one to answer, and the scientific evidence still doesn’t point at any clear answer. On the whole, lime trees probably do benefit bumblebees, and only one species - Tilia tomentosa is regarded as being very harmful, the others less so. Lime trees also bring great benefits to the other kinds of wildlife that use them, so we certainly wouldn’t recommend cutting one down. There is a bit more information on this on our website, here: http://bumblebeeconservation.org/about-bees/faqs/#row9
BBCT Outreach Officer