I apologize for any assumptions I may have made...
In iMovie, Start a New (*empty*) Project (Create New). iMovie asks what Library to create the project in. If you have a bunch of Libraries, pick a small one and click OK. Click the Titles selector. Drag Line Lower Third into your project timeline. It should be the *only* thing in the project.
Immediately go to: Send Movie to Final Cut Pro.
FCPX will Open the iMovie Library you created the iMovie Project in and with the Event already selected in which the "Movie" you sent is in.
Double click on the Project from iMovie. (It has a "Clapper" or "Slate" icon).
It opens the project in the Storyline. In the storyline, ONLY your iMovie title should be there (Line Lower Third has Transitions already attached on either end -- I'm not counting those as separate! But they will not copy/paste with the Title, so no need to bother.)
BTW - at this point if FCPX hangs, don't sweat it. Command-Option-Escape and force quit, then restart it. If you have to do this, you will probably end back up in a previous project you were working on in FCPX. Navigate back to the iMovie Library >Event > Project and open it up again by double clicking on it.
Skim the storyline to make sure the title is working. (And -- it really is a title -- I get back to this.)
Click the purple object (Title) in the storyline and Copy it. (Just Command-C. This is the only way you can move it out of this iMovie Library project).
Go to another project (or back to the one you were in before sending the iMovie "movie") from your FCPX Library and open it in the Storyline. Position the playhead at the point you want to add the title.
Go to the Edit menu and Paste as Connected Clip (or type Option-V). Your iMovie Title is now attached to your storyline (and it is transparent!) Select the Title.
In the Inspector, you will see a small icon with a Capital T in it — that is this title's inspector. There is only one published parameter (labelled "ligature" -- it's not even capitalized -- but other iMovie Titles will have other available parameters depending on what was published.) [PS - I was working on transfering Organic Main while writing out these instructions -- it has Build In/Build Out/ Font, Size and Text Color options... just like a regular FCPX title!]
At this point, you have a working iMovie Title in your FCPX Storyline. You can edit its texts in the Viewer or in the Text inspector (after selecting the individual texts in the Viewer).
In order to *keep* this title in FCPX for further use later on, you're going to want to save it in an Event. I recommend creating a New Event in FCPX and call it iMovie Titles so you have an easy way to find them later (there's actually several worth going after) — because these titles are NOT added to the Titles Inspector like all the other FCPX Titles — it will be an "orphan". About the only way you can do this is to right click on the iMovie title in the FCPX Storyline and select New Compound Clip and in the popup dialog, send it to the Event you want to save it in (again: recommend iMovie Titles event).
So after the first use, when you want to use the title again, you will go to the Event you saved the compound clip in, select it and type Q to connect it to the storyline at the playhead OR you can simply drag it into the storyline and place it where you want it. THEN, (whew) in order to edit the Text, you will have to go to the Clip menu and select Break Apart Clip Items (or type Command-shift-G) to "liberate" your title from the compound clip. (This action will not undo the compound clip saved in your Event!)
This is the only way to keep a copy of iMovie Titles in an FCPX Library so that you don't have to keep reopening the iMovie Library in FCPX.
When you're done saving the title as a compound clip, you can Close the iMovie Library if you don't want it hanging around. If you don't mind having it open in FCPX, then you don't need to mess with the compound clips, you can just reopen the iMovie Project and copy the title back out, then Paste as Connected Clip in a storyline.
A "Compound Clip" is any media you want to collectively have saved to an Event. In this case, it is just one object - the title, but it can be a group and/or string of clips selected together. It can also be a method to use to maintain specific timing when stretching or shortening a clip or effect will speed up or slow down (as can happen in Titles and Generators) - you are able to edit (trim) a Compound just like any other standard clip on the "outside" while all the timing of clips and effects are maintained on the inside. You can also use a compound clip to apply Effects that will affect *every* clip inside in one "throw" so to speak — so a way of adjusting multiple clips with just one effect. Compound Clips are very versatile.
HTH