When the devnagari or hindi font was used on Lyx, the font appear as a garbage on Lyx GUI. This can be easily seen by pasting "इस पृष्ठ पर इन्टरनेट पर उपलब्ध विभिन्न हिन्दी एवं देवनागरी सम्बंधित साधनों की कड़ियों की सूची है। इसमें ऑनलाइन एवं ऑफ़लाइन उपकरण शामिल हैं।" on lyx document. What can be done to improve the appearance even if pdf generated is properly rendered. Here is the minimal example http://wiki.lyx.org/uploads/Windows/Devanagari/Devanagari-Test.lyx
Perhaps you just need to update your LyX version. I have no idea if the following are correct, but they do not look like "garbage" to me (it looks quite pretty to me). Can you confirm that it is the correct output?
The following is from both LyX 2.1.2, which seems identical to the output from the development version of LyX (2.2.0dev). My OS is Ubuntu.
Here is my LyX output from Devangari-test:
Here is my output from pasting the text that you had in your answer: