Not easily.
There are some individual words in common (“bad” = schlecht in both Lux. and German; ditto “boring” = langweilig), and some words are fairly close (“maybe” = vielleicht in German, vläicht in Lux, which sounds like the German word if you apostrophize the first diphthong; “together” = zusammen in German, zesummen in Lux). Other words are clearly related when you know (“but” = aber in German, pronounced like ‘obba,’ vs awer pronounced ‘ovva’ in Lux; “to drive” = fahren in German vs fueren in Lux; “child/children” = Kind/Kinder in German vs Kand/Kanner in Lux), but the sound is sufficiently different that it slides past the ear.
Plus the verb conjugation in Lux. is all wonky compared to German. The infinitive form of most verbs ends in “-en,” like fahren above, or spielen, “to play.” Except for irregulars, you normally use that form with the subject “we” or “they” — wir spielen, sie spielen. But in first person, you conjugate: ich spiele. By contrast, in Lux., you use that infinitive form in first person: ech spillen. The infinitive “to be” in German is sein (“zyne”), which becomes sind for we/they, but in first person, you say ich bin (I am). In Lux, you say ech sinn.
Plus there’s a fair amount of vocabulary taken from French and Dutch. For example, if you want to refer to a work rotation in German, you might say die Rotation (“dee roh TA see OHN”). But in Lux, you use a French-derived word — Roulement (capitalized because it’s a noun).
If you put written German and written Luxembourgish next to each other, you can pretty easily map one to the other (er wohnt in einem Haus → hie wunnt an engem Haus → he lives in a house). But when being spoken, all these little differences add up. The German speaker hearing Luxembourgish will notice words every now and then they recognize, but the overall effect is that it sounds like a drunken soup of almost but not quite German.
The Luxembourger listening to a German speaker, by contrast, will have no trouble at all, because the Luxembourger speaks German. And French. And English. And probably some Portuguese. And… 