I am making a logo for a company that is an Ltd. - does the Ltd. need to appear in the Logo itself? The logo is a combination of text with a graphic worked in beneath it.
It would be the designer's choice how much to emphasize "limited" or "Ltd.", unless the client has specified something. Technically, the "limited" is part of the company name.
Some companies include it, others don't.
You can also choose to spell out "Limited" rather than using the abbreviation.
There are examples of others that go a different route. For example Adobe Systems Incorporated, does not use the full company name for any logo: