There are significant differences in the image quality/IQ and overall sharpness of the LX7 when one is shooting at lower (or so-called 'base') ISO's - and higher ones.
The lowest ISO the LX7 has is 80 - but shooting in conditions (usually well-lit) at ISO 100 often yielded truly superb images for me. Here's one taken in the high desert of eastern Oregon on a cloudless day -
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Airstream 1 by
La Chachalaca Fotografía, on Flickr
And another, taken in late summer on my street in the small rural Oregon town where I live, just before a storm -
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July sky by
La Chachalaca Fotografía, on Flickr
In this shot, taken at an art exhibit at the local library, you can see the general sharpness of the lens, almost wide open -
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Mannequin #1 by
La Chachalaca Fotografía, on Flickr
At higher ISO's, the image quality isn't as stellar - but I always found it generally good - or at least, 'good enough'.
This was taken at ISO 400, almost wide open -
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Pinball Machine (Danger Bridge Out) by
La Chachalaca Fotografía, on Flickr
And the ultra-fast lens truly has some nifty low-light capabilities.
This shot was taken with available light, in a Cathedral in Guadalajara, Mexico, which shows another aspect of the LX7, its versatility as an inconspicuous small 'street' camera in places where a larger or more ostentatious camera might stand out too much -
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en la Catedral by
La Chachalaca Fotografía, on Flickr
As long as we're on the subject of the LX7's virtues, it has a truly brilliant Macro mode - which allows shooting in ridiculously CLOSE close-ups - and getting the kinds of angles and images which, normally, on other cameras, I would need either close-up lenses or a dedicated Macro lens to achieve. I also think that the smaller sensor tended/tends to give some images a slightly grainier - closer to a 'film' look - than bigger-sensored cameras --- which I always appreciated.
This was taken in 'Macro' mode -
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Mushrooms by
La Chachalaca Fotografía, on Flickr
This is a low-light selfie, taken almost wide open, showing that in spite of the small sensor, even at a wide angle, the lens is capable of some slight background bokeh -
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Self-portrait (color) by
La Chachalaca Fotografía, on Flickr
I had mine for years and years and for quite some time, found it to be an almost ideal semi-pocketable high-quality travel camera. I've now replaced it with an equally small Canon EOS-M which does some things better than the LX7, and others not quite as well. But at the same time, I must say that I've taken some of what I think are the best photographs I've ever taken with my former LX7 - so overall, if you can live with its 'deficiencies', it's not only an excellent portable travel camera - but a fine photographic image-maker in its own right.
And no, it's not a perfect camera. But it does a lot of things very well.
Hope this helps