Font selection in TeX is a little different from that of MS Word. In LyX, the following choices are available:
Changing the default font size of the document: Under Document>Settings...>Fonts, you can choose the Base Size as being Default, 10pt, 11pt or 12pt (Default is 10pt in most cases). This is similar to the traditional \documentclass[<fontsize>]{<doc-class>} selection in LaTeX.

For changing font size "on the fly" within the text: Select the text, click the Text Style button
(or Edit>Text Style>Customized...) and choose one of the Size options (Small, Normal, Large, etc.). Click OK or Apply to activate the font selection.

Under the Base Size of 10pt / 11pt / 12pt (respectively), the following font sizes (or Text Styles) hold:
Tiny (LaTeX's \tiny): 5pt / 6pt / 6pt
Smallest (LaTeX's \scriptsize): 7pt / 8pt / 8pt
Smaller (LaTeX's \footnotesize): 8pt / 9pt / 10pt
Small (LaTeX's \small): 9pt / 10pt / 10.95pt
Normal (LaTeX's \normalsize): 10pt / 10.95pt / 12pt
Large (LaTeX's \large): 12pt / 12pt / 14.4pt
Larger (LaTeX's \Large): 14.4pt / 14.4pt / 17.28pt
Largest (LaTeX's \LARGE): 17.28pt, 17.28pt / 20.74pt
Huge (LaTeX's \huge): 20.74pt / 20.74pt / 24.88pt
Huger (LaTeX's \Huge): 24.88pt / 24.88pt / 24.88pt
Increase: Step one font size up
Decrease: Step one font size down
Reset: Same as Normal
For specifying and using other font sizes, you will have to include packages that support this or add LaTeX code within your document where you want these changes to take effect. For example, the best way to accomplish this is to use Latin Modern via the lmodern package. Insert this in your LaTeX Preamble using

and then insert the LaTeX code (via Ctrl+L or
) \fontsize{40pt}{48pt}\selectfont where you want it to take effect. \fontsize{<size>}{<baselineskip>} sets the font size to <size> and the skip from baseline-to-baseline as <baseline>. it is usually accepted to have <baseline>~1.2x<size>.Note that this command is considered a switch, making all subsequent text that size. If you want to localize the change, you need to use grouping via braces {...}. For example, the LyX input

yields

A similar approach can be followed using the anyfontsize package.