Inline elements apply to individual characters rather than to whole lyx environments. This is lyx's weakest area.
Emphasised text looks like this. You can can turn emphasis style on or off using the Toggle emphasize button. The button's icon, an exclamation mark, appears depressed when emphasise is on. Turning emphasis on will emphasise the currently selected text. If no text is selected, all text typed after the current insertion point will be emphasised.