Broken stem tube – LBS "just" lowered handlebars. Is this safe?
Here's how I would fix the problem.  This could all be done by somebody with basic tools and basic knowledge.  

Get a quill-threadless stem adapter and a new stem. This will allow you to fit the new stem to the handlebars without removing anything from the bars. The old stem can be removed destructively by removing the cinch bolt and prying the thing apart since it is already broken and no longer fit for use. 

Using a new theadless stem will give you a huge variety of stems to choose from so you can find the right length and angle to fit you comfortably and match your riding style.

I'm not recommending those specific products, but those are the type of products you should be looking for. Make sure the handlebar end of the stem is the proper size for the bars you already own.

I got a threadless stem adapter a couple years back for my old bike and it makes working on anything to do with the handlebars so much easier.