Most probably you have checked by error the Draft mode
in the LaTeX and LyX options
tab of the Graphics dialog:

You can check also if the image have this option in the Code Preview Pane
, (View menu):
\includegraphics[draft]{example-image}
Maybe you have set the option at a document level:

And then you must see in the Code Preview Pane some starting code as:
\documentclass[draft]{article}
Improbably, you could have this global option in the graphicx package, because set this is not trivial with LyX menus: Document → Settings → Local layout → type provides graphicx 1
→ Validate → Apply, then in LaTeX preamble → type → \usepackage[draft]{graphicx}
→ Apply.
Finally, if there are not any draft
option anywhere, but the image is not still showed the PDF, the file does not exist, or you set the wrong path and/or the wrong filename.
At this respect, just some suggestions to debug this kind of issues:
Place the images in the working directory.
Be sure that you do not set absolute paths (C:\etc\etc...
) in the Graphics tab, but only relative paths (if you follow the above point, the relative path is just the file name).
Use short and simple file names (No spaces, no underscores, no extra dots, no tildes, no mix under-upper cases, no nothing). Although actual programs supposedly can handle well all of this, live is simply easier without having to deal with hypertrophied file names.
draft
option, or the pictures are not found, check the log-file./Users/muthukum.../Documents//Thesis/Muthu/thesis/fig1_1.pdf
that got mangled in the conversion process. Is that possible?draft
from\documentclass[...]
.final
is the default option.