Honestly, I would log the fact that she has fallen asleep on her own twice as important and possibly a sign she is ready, IF she wasn't just responding to being extra tired because of the holidays.
There is quite a bit of debate about when babies should learn to fall asleep on their own - my daughter took forever to learn to fall asleep completely of her own accord. Most sleep training methods I know, recommend against "crying it out" until after the sixth month of life, but there are a lot of in-between ways to handle things. Some people say they should never fall asleep when it isn't on their own and that you should get them to the point where the are almost asleep and then lay them down. There are tons of books all with their own ideas, and there are a number of sleep studies that conflict with one-another as well. As a result, there is quite a debate about how to "sleep train" and this can be one of those hot-button issues with parents too. So, I don't know that there is one ultimately awesome answer to your question When should we start trying to lull her to sleep in her bed? other than, when it seems right to do so for your family with your specific situation.
With my daughter, we didn't have her fall asleep on her own until much later. We still had to sit in her room with her while she fell asleep at two years old - which wasn't ideal. However, once asleep (which took hardly any time at all) she was asleep all the way, slept well and deeply for longer than most of her other two year old friends and we never had fights about nap time or bed time - but that was what worked well for us. My sister-in-law hastled us and said we should have had her sleeping on her own much sooner - she scoffed about it actually and acted as though I was a lesser mother because I hadn't properly "sleep trained" my child. Her advantage was she could simply close the door and expect her two-year-old to go to sleep at the end of their sleep routine. It did require less of her time in her child's room, but his naps weren't nearly as long, and they did have more debate when it was time for bed, more "stalling" techniques happened later on in life - but that was what they felt worked well for them. All in all, both sets of kids slept and got the proper number of hours, we both probably spent an equal amount of time working with our kids toward sleep, it was just spent in different ways.
Having said that, I will say, that if she is falling asleep "on her own" right now, why not try putting her down just before she falls asleep from here forward? If it doesn't work, you can go back to the old way and no harm done. The way to tell they are "almost asleep" but not quite is by watching for a point when they go pretty limp and have what I can only describe as a "blank stare." Gently place her in her crib at that point in her preferred sleep position and see if she is willing to drift the rest of the way into sleep on her own.
I will also refer you to these questions that may have helpful information for you right here on SE.
Help with Sleep Training
My 14 week old is waking frequently, can we sleep train yet?
I'd also like to refer you to this wonderful blarticle 6 Little Secrets of a Sleeping baby that is enlightening.
It re-iterates the fact that crying is a natural thing, being emotionally attuned and available helps baby sleep longer and more deeply even if crying has to be part of the journey, that communication is critical and that it encamping oneself in one side or the other on any parenting issue is probably not healthy for anyone among other things. It gives tips and advice that are super general, but soothing for parent and if it soothes parent, it probably helps in soothing baby too.