Learn Spanish (Latin America): Terminaron la restauración a lo grande. - They finished the restoration in a big way.

This sentence uses the structure a lo + adjective to create an adverbial phrase of manner, which tells you how an action was done. It translates roughly to "in the style of" or "in a [adjective] way." So, a lo grande means they did it in a grand, impressive, or "big" way.

If there were multiple restorations, would it change to a lo grandes?

No, the adjective in an a lo phrase is fixed and does not change to match the number or gender of the subject or the object. Because it functions as an adverb (describing the verb Terminaron), it always stays singular. You would still say Terminaron las restauraciones a lo grande.

Could I use an adverb ending in -mente, like grandemente, instead?

You could, but it changes the meaning slightly and sounds much less natural here. Grandemente usually means "greatly" or "to a large degree" (like being greatly affected by something). If you want to say something was done "in style" or with a lot of flair, a lo grande is the go-to phrase.

Why is Terminaron in the preterite tense rather than the imperfect?

The verb terminar (to finish) inherently refers to the specific endpoint of an action. Because finishing the restoration is a completed event that happened at a specific point in time, the preterite tense is required here.