Some thoughts on the matter.
I cannot speak as much for the LX7, but I do have the LX5.
The main differences between are the MOS sensor instead of CCD, larger pixel screen, burst rate, aperture ring, larger aperture range (f/1.4-2.3), and built-in ND filter.
If you are worried about the provided lens cap, you can get a Ricoh GXR-like, automatic lens cap for the LX7. This lens cap does make the the LX7, a bit thicker from front to back.
I also picked up a RX100 for cheap ($349 US) after getting the Ricoh GR.
Both cameras have a solid feel, with no sign of creaks compared to some of the plastic bits of the GR (although it is a mostly magnesium alloy build).
The thickness of the RX100, along with the GR, both fit nicely in a coat pocket. The LX7 would fit a bit tighter with the provided lens cap.
You would most likely be using a strap for the LX7.
If you plan on taking photos or video footage at a club event, or concert, the RX100 may be of better use.
It can pass as a compact point and shoot though security, while the LX7 looks almost as big as a smaller Micro 4/3 camera (well except the GM1).
The RX100 images at higher ISO ratings will be better as well.
The usable range would be for the LX7 would be at 100 base to 800 ISO max. 1600 ISO might be okay.
You have lot more to work with in the RX100's 20.2 MP for cropping. The LX7 is rated at 10 MP, but that is in the 4:3 aspect ratio. It will be 9.5 MP at a 3:2 aspect ratio.
Ergonomically speaking, I prefer the LX5. The size and grip are more comfortable even for one-handed use.
The RX100 is like a bar of soap, it is an absolute must to use the hand strap and get a stick-on grip.
A Richard Franiec, Sony AGR1, or Flipbac G2 grip would be recommended.
The external controls on the LX series are easier to access and configure with a dedicated exposure / focus lock, ISO, and timer buttons. Macro & manual focus is available as a switch on the front of the camera, and aspect ratio switch is right beside it.
The combination rear control wheel / pad of the RX100 has to configured from the start, otherwise you will waste your time menu-diving to get to access a function.
The Fn button similar to the LX5's Q. Menu button to access a customizable function menu such as white balance, ISO, flash sync, metering mode, and focus mode.
On the rear control wheel / pad, I have the center button set as exposure lock, left button as drive mode selection, and right button for flash mode.
I wish the power button was either recessed, or a switch not so close the shutter button. I have had few times when the RX100 would be accidentally powered on my in coat pocket.
I also hate that they placed the HDMI port right next to tripod mount.
One thing I like on the LX5 that I cannot find on the RX100 menu, is a step-zoom equivalent.
I can step zoom lengths to 24, 28, 35, 50, 70, & 90mm, like using a prime lens on a 35mm camera.
The flash can only be popped up through function selection on the RX100. The LX5 & LX7 has its own external switch. However, the flash can be pointed up to bounce the flash off a ceiling on the RX100. The flash only faces forward on the LX cameras.
The LX7 probably has a better set of optional accessories like the an OVF, EVF, several flashes and a screw-on adapter for a circular polarizer.
The RX100 has an optional adhesive-backed filter adapter to mount to the front of the lens.
You have to spring for a RX100 II to use an OVF, EVF, or flash unit.