I have never been in the area, but from what I can see in the Internet, there indeed are a lot of winter hiking routes in Lenzerheide. And all those routes are signposted. In fact, you can see a map and get all the hike descriptions right here: https://lenzerheide.com/en/winter/winter-activities/winter-hiking/winter-walking-tours
I would recommend starting with the hikes that are rated as easy, and if you are having no problems with those, you can upgrade yourself to the ones of moderate difficulty. The difficulty usually describes the distance, and the hight meters, but can also be because of technical difficulty, so read the description well.
While there is no danger to females or any other human beings from either wildlife or other people in Switzerland, one should not underestimate the mountains. Even more so in winter. Make sure you will be able to walk down on your own, or catch a lift down before its closing time. Make sure you have enough clothes and something to drink.
One more important thing to pay attention to while in the mountains in winter, are the avalanches. While most hikes should be put in places that are safe, do read descriptions or ask around to be sure. Also, on different days the avalanche dangers might vary. General avalanche dangers can be checked here: https://www.slf.ch/en/avalanche-bulletin-and-snow-situation.html#avalanchedanger. Ask around and do not go on hikes that are closed. They usually are closed because of avalanche danger.
With regard to clothes, make sure that you are wearing layers of clothing that are easy to take off/put on. You do not want to get cold, but you also do not want to sweat. Take some extra base-layer clothes if you are planing to get a break in a hut. You will probably sweat in any case, and it is nice to change into something dry. Walking with just thermo leggings might work, but be sure to bring along something waterproof/warmer. The weather in the mountains is likelly to change, and you do not want to risk.
You should not worry too much about the lifts though, because either the accomodations are already made for pedestrians, or you will not be able to get on them. Most lifts where pedestrians are allowed will be cabin lifts anyway. And if you will need to take a chair lift, the lift guys will be aware of you. You probably can see what kind of lifts (if any) you need to take in the descriptions of the hikes.
You did not ask anything about the equipment you should take, but I will give some tips anyway. You should absolutelly bring some sticks. This could be either normal hiking sticks equiped with snow baskets, or just a pair of regular ski sticks. While most of the hikes can probably be done in waterproof winter hiking shoes, you might consider renting snow shoes for easier walking. This could be especially useful with fresh snow. Some of the hikes will, however, be on roads, you do not need snow shows for these.