Thank you for providing links to sample photos, and from what I can see, I don't think the LX100 will be adequate for emulating these.
Instead of depth of field, I think a better measure is the amount of background blur, which is typically what people are looking for. The amount of background blur in your sample photos are often between 3 and 4 times what the LX100 can deliver.
A very simple measure of potential background blur is proportional to the focal length divided by the f/stop value, which is the "entrance pupil width" of the lens, or the size of the optical opening in the lens when viewed from the front of the lens.
The advertising literature for the LX100 only give full frame equivalent focal lengths, not actual focal lengths. The actual focal lengths are 10.9 mm (at f/1.7) and 34 mm (at f/2.8), which gives us pupil widths of 10.9 mm / 1.7 = 6.4 mm, and 34 mm / 2.8 = 12 mm. These values are considerably smaller than the pupil widths in most of your sample photos, although much larger than high-end smartphone cameras, which have to resort to digital trickery to get blurry-looking backgrounds in portraits.
Background blur is also highly dependent on how far away is your background, and you'll get a nearly maximum effect if the background is at least ten times the distance to the subject. The blur is also proportional to the magnification of the subject on the sensor, and so limiting the field of view at your focus distance is important as well; be sure to fill the frame with your subject.
Examples of pictures I would like to be able to take :
Example 1: (blur on medal)
https://www.pexels.com/photo/photo-of-woman-wearing-white-top-2811087/
This was taken at 85 mm at f/2, which gives us a pupil width of 42.5 mm. The LX100 can't give quite the narrow angle of view as this lens, but the closest gives us only a 12 mm pupil width, meaning that you'd get about 3.5 times as much background blur with the Canon.
But this image does not have a background that really needs blurring. As Klaus mentioned, a nondescript background can substitute for blur. Blurred backgrounds are an artifice that photographers can take advantage of—in order to isolate and emphasize the subject—but we don't actually see blur in real life. While many photographers consider this a useful artifice, there are others who reject it due to it being unrealistic, and so they put much effort instead into finding good backgrounds.
example 2 :
to isolate a person in a group : at 10 feet (or less) , I would appreciate to be able to manage a depth of field of 5 to 10 inches.
https://www.pexels.com/photo/woman-wearing-white-and-pink-hijab-1122679/
This image was taken with a focal length of 55 mm f/1.8, which gives us an entrance pupil width of 30.6 mm, which again is significantly larger than what the LX100 can deliver.
This is 35 mm at f/1.8, or a pupil width of 19.4 mm
This is 50 mm at f/1.4, which gives us another large pupil width of 36 mm, giving a much blurrier background than the LX100 can deliver.
The cat photo has maybe double the blur, while the last two photos are the only ones that the LX100 could nearly duplicate, as they have only slight background blur. This is a useful comparison tool:
Free tool to compare depth of field and background blur capabilities across different lenses, apertures, and focal lengths
www.howmuchblur.com
But again, you have to use the
actual, and
not equivalent focal lengths. To calculate actual focal lengths from equivalent, you divide the equivalent value by the camera crop factor, which in the case of the LX100 is 2.2, and so 24 mm equivalent / 2.2 = 10.9 mm actual.
The LX100 is a well-regarded camera, and many photographers don't miss its lack of ability to strongly blur backgrounds. It has a fairly large, low noise sensor as well, so the images will be rather clean, even in somewhat low light.
Also, if you do instead consider a larger sensor interchangeable lens camera (which is what I use), understand that lens quality will be important when shoot wide open: many ordinary f/1.8 or f/1.4 lenses suffer from lots of aberrations at wide apertures, and they may have distracting, jittery background blur or bokeh, which kind of ruins the viewing experience.
