There are a few other problems which could occur should a 3.7V cell be substituted for a LiFePO4 cell. One is overcharging. When it comes to Li-ion batteries, LiFePO4 is somehat unique in that it tolerates overcharging significantly better than 3.7V chemistries. This means that manufacturers of garden lights can get away with very minimal charging circuitry compared to what would be necessary for safe operation of a light with a 3.7V cell. In other words, substitution with a 3.7V cell could result in a rather dangerous overcharging situation.
Driving circuitry is another potential problem. LiFePO4 naturally has a lower voltage (3.2V nominal) compared to other Li-Ion chemistries. This lower voltage allows an LED to be easily direct driven from a single LiFePO4 cell. Much like the absence of sophisticated charging circuitry, this reduces costs. Using a 3.7V cell would not only overdischarge the cell (as mentioned above). It would also likely overdrive the LED, which would burn it out.
Finally, there is the issue of heat. By their very nature, solar garden lights sit in the sun and get hot. They therefore need a battery that is tolerant of heat, and will neither experience significantly decreased longevity in the heat nor be more likely to experience thermal runaway. This pretty much rules out the more delicate 3.7V chemistries.
The bottom line? Solar garden lights are pretty much designed around the lower voltage and more robust nature of LiFePO4 batteries vs 3.7V cells. If you need to replace a bad cell, it is DEFINITELY best to replace it with another LiFePO4 cell.