I assume you mean an LR (low resistance) atty, not LV (low voltage). I do not know of any LV attys, since they are generally catagorized in terms of ohms, not volts. Also, all Li-ion batts are 3.7V, but their capacities can be very different, as well as the circuitry which dictates the voltage on the coil.
The issue with LR attys is due to the fact that they draw much more current than a regular atty. For this reason batts with lower capacity can become over-taxed and die fast, not just in terms their "duty cycle" (time between recharges), but their lifetime in general. Generally manufacturers strongly suggest using LR attys only on batts with greater than 450 mAh. People have reported using LRs on 510 mega batts (280 mAh), but the atty drains the batt entirely very quickly, in fact so quickly that it may well damage the insides. Batts in general have about 300 cycles, but a current-damaged batt may have much less before it cannot be recharged well.
The lowest capacity batt that I know of where it is "ok" to use the LR atty is the eGo/Tornado batt, which is 600 mAh. Again, however, the LR attys drain any batt much faster than a regular atty.