Lime is prized by wood carvers because it is fairly soft and featureless, which is more or less why most wood turners don't bother with it.
With hard, dense timbers the wood fibres immediately ahead of the cutting edge, hold firm and support those fibres which are already being cut or sheared by the cutting edge, so fibres cut relatively well. However, with soft timbers of low density, support from neighbouring fibres is minimal, so the fibres being cut/sheared by the cutting edge are more prone to being pulled out of the surface rather than being cleanly cut or sheared away. Do yourself a favour....put timbers like lime away until you have perfected light, shearing cuts and good sharpening of your tools.
There is no one, specific timber that you should use, but for now, just stick to medium density timbers, such as sycamore, beech etc; they are both good timbers for beginners (there are many more)
Les