What's wrong with:
1. using offset
2. using graph custom lfo
3. using a hydra in between to make sure it travels only in the wanted range
4. formula device, on its own or in between the lfo and whatever you modulate
what exactly do you want to achieve? I.e. how do you want a sine or saw or so act on another parameter? Try to see it visual, as curves.
But I also know your pain, the lfo is a bit off the other modulation devices with its silly amplitude and offset tunings. I normally make it cycle in the full range and then use a hydra in between to set the actual range I want to modulate.
An artificial threshold, with a formula device, would alter the shape of the modulation. But is possible too, either clipping the original shape or wrapping it around between positive/negative at center or a threshold you want.
This stuff can be a bit confusing after all, because the meta devices act not absolute, but mostly relative.