Should I learn some Lithuanian before going to Lithuania?

The short answer is "no, don`t bother". People will most likely not understand you anyway, and even if they do, most of them will be laughing their asses off over your terrible pronounciation. That will probably settle the case for most people, but there are always some stubborn individuals who percist in defying both authorities and common sense once they have gotten an idea in their heads. For those pig-headed polyglots I have only one thing to say: "Have at it!". Here are a few tips along the way:

1. Speak loud and Clear. Shout if you do not find it inappropriate

Bring me some CEPELINIAIAI!!! Your hand written Samogitian menus do not scare me!

2. Have confidence. Preferably overconfidence

You need to seem convinced that you are speaking correctly, in either one language or another. Speakers of Lithuanian can smell inconfidence and interpret it as a sign of weakness. If bread is pronounced DUUUUUNA from your perspective, then stand your ground. They will eventually understand.

"KURR TOOOOALETTASS?"

Just give it some time, and people will understand.

After all, these people even manage to understand EACHOTHER.

3. Be immune to laughter

Remember that Lithuanians are not supposed to smile or be happy in public, and maintain a serious face. They too will soon remember this and stop laughing. Also remember that you willingly put yourself in this situation.

"GALLUUU HIER ZU PARKIERAMS???"

You are of course being ridiculous, but she might rather let you park on her lawn

than risk being seen laughing in a public place

4.Go with what you know (or think you know)

If you can provide a nice bouquet of words that are more or less correct for the occation, some bystander gifted in riddles will eventually figure out what you want.

Aš nori WEATHER COCK zu pirkt!!!

Anyone trying to sell this overpriced product will get you at once

5. If all else fails, switch to PR English and speak it PERFECTLY

Try using the most difficult and uncommon words that you can think of (preferrably try to channel Steven Fry). This will remind them of their own short-comings, and will usually result in a much more undertanding atmosphere. (This one actually helped me out of a traffic ticket once)

"Jevvla møkakjering so gje meg sild og ost i syltetøyglas

når eg klart å tydele har bestilt kjøtbolla. Skulla hatt i rævæ me øks"

OR:

"Dear lady, I believe that there has been a minor mix-up with regards to the orders leading up to this meal. You see, I do not so much crave herring as I am inclined towards a more meaty-type dish. And I believed that to be our mutual understanding of the situation.....hmmm? Am I much mistaken...? 

PS: Never leave a potential insult hanging, so if you think the waitress is seecretly ridiculing you in her native Sanskrit-like language while leaving your table - curse her right back in your local dialect! Insecurity works both ways.