Using LyX or Word, you never should use white spaces to add indentation to the first line of a paragraph. This bad habit is prone to errors and if you need change the layout later, you must change manually each indentation. Unlike Work, LyX (LateX) fortunately avoid you do that with normal spaces.
The indents can be adjusted globally for all the document is Word or LyX. In LyX (LateX) however, according to your language settings, the indentation by default could be omitted in the first paragraph after a section title.
The way to do so in Lyx is go to Document > Configuration > Text Layout and set the paragraph indent and paragraph vertical spacing. The first menu should allow you to insert in the source preamble settings like \setlength{\parindent}{2cm}.
Another option is go to Document > Configuration > LaTeX preamble and insert directly some like \setlength{\parindent}{1em} o their raw TeX equivalent \parindent0pt.
You can add extra indents Ctrl+L\indent or via Insert>Format add special spaces like \, \, or ~. Note that these spaces could be ignored also in the first paragrah, but you can insert in ERT boxes many other spaces like \quad,\hspace{3cm} or even \mbox{~~~~~} that are not ignored in any paragraph.
\indent, or with\hspace{\parindent}, or with\hspace{15pt}, or... – Werner Jan 28 '15 at 05:01