In my opinion the perfect solution for a quick and semi-private deployment: Dropbox can host a static site placed in the /Public folder. Just keep the log directory anywhere on your PC, but preferably somewhere in a private section of your Dropbox, edit the _config.yml and specify

destination: ../../Public/mylabnotebook

i.e. the relative path from your blog directory to the target directory. Then build your blog.

jekyll build

Now, wait for the sync to happen and go to your Dropbox account online, navigate to your public directory, and there to the newly created directory mylabnotebook. Right-click on the index.html file to get the public link. The root of this link (without /index.html) will be required for the next step:

Go to your _config.yml file and set

url: "https://dl.dropboxusercontent.com"
baseurl: "u/xxxxxx/lablog"

Now build again and navigate in your browser to https://dl.dropboxusercontent.com/u/xxxxxx/mylabnotebook/index.html

Save this long, cryptic link as a bookmark or to load at browser start-up. For the future, all you need is to re-run the simple jekyll build command each time you updated a file (which also can be done by a simple bash script or a background process that listens to changes; you’ll figure that out later)!