IF you embed any ICC profile, sRGB or otherwise, an ICC aware application will match what you see in LR and Photoshop etc. If it doesn't match, that's your problem. Try with something quite different than sRGB (say ProPhoto RGB), the image will mismatch even worse. Using sRGB alone isn't the answer. Non ICC aware applications have no idea what sRGB means, they don't understand the profile that is used by the display to provide color managed previews etc. Not being a Windows user, I can't tell you for sure if the applications you're using are color managed or not, or if they've been configured for this if possible.
You have Photoshop right? Do the images you export from LR match in Photoshop? They should indeed. Again, if they do but not the other applications you mention, then those other applications are the problem. And again, here's why sRGB alone doesn't fix that problem:
sRGB urban legend & myths Part 2
In this 17 minute video, I'll discuss some more sRGB misinformation and cover:
When to use sRGB and what to expect on the web and mobile devices
How sRGB doesn't insure a visual match without color management, how to check
The downsides of an all sRGB workflow
sRGB's color gamut vs. "professional" output devices
The future of sRGB and wide gamut display technology
Photo print labs that demand sRGB for output
High resolution: http://digitaldog.net/files/sRGBMythsPart2.mp4
Low resolution on YouTube: https://www.youtube.com/watch?v=WyvVUL1gWVs