The Station Agent
Lars and the Real Girl
Pieces of April
Winter Passing
In America
Winter's Bone (much darker and violent)
While You Were Sleeping (lighter and funnier, but still poignant)
I agree with these ones that have been recommended by other people.
Her
Like Crazy
Somewhere
Up in the Air
Eternal Sunshine of the Spotless Mind
Anyone notice what the first 3 movies at the top have in common?
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American Beauty, by Sam Mendes
(Both films are about the dissatisfaction with one's life and include a relationship between a middle-aged man and much younger woman.)
Consequences of Love, by Paolo Sorrentino
(A film about loneliness and a developing relationship between an older businessman and a young waitress.)
A Single Man, by Tom Ford
(Loneliness as felt by a man who lost his long-term partner.)
Her, by Spike Jonze
(A story of a man who develops a relationship with a computer operating system.)
Broken Flowers, by Jim Jarmusch
(A bachelor learns that he might have a son with one of his exes and embarks upon a trip around the country to get to know him. It also stars Bill Murray.)

The Girl in the Cafe
Please watch this movie. There are a lot of similarities to Lost in Translation.

American Beauty gives me this feeling.

Copenhagen. Seriously. Isolated & lost man in love with a younger woman. Great acting.

Before Sunrise/Sunset
In Search of a Midnight Kiss
5 Centimeters per Second
Her
All About Lilly Chou Chou
Tony Takitani
Broken Flowers (Also starring Bill Murray)
The Hottest State
Like Crazy
Mary and Max
Japanese Story
Whisper of the Heart
"Our critique began as all critiques begin: with doubt"

Before Sunrise

Once. It's not a fish out of water movie, but it has the isolation and loneliness vibe.

One that hasn't been mentioned is
"The Way."
It's a similar type of "Road Movie" where strangers are together on a journey. It's gorgeous film.

Never say never

And let's not forget both movies are just beautiful to look at! (although in very different ways)
"Hold on, boys! I, for one, would like to hear what the blood-spattered young lady has to say."

I found Anomalisa to be very similar in some regards.
Both are about a depressed man, completely alienated from their families.
Both men are fairly successful in their respective fields of work.
Both are staying in a hotel, spending their nights in the bar, lonely until they find a woman they form a special connection with.
And in both cases it doesn't last.
"Hold on, boys! I, for one, would like to hear what the blood-spattered young lady has to say."

Last Tango in Paris. Can't believe it wasn't mentioned, maybe it's not so similar.
I like that boulder. That is a nice boulder.

Her
Sideways
Little Miss Sunshine
Garden State
Big Fish
Into The Wild
Ghost World
Feel your heart beat.

Millenium Mambo
Fallen Angels
Chungking Express
3-Iron

First movie I thought of was 'Closer' with Jude Law and Natalie Portman. If you liked Lost in Translation, you'll absolutely love Closer.

A lot of good recommendations from others.
I'd like to add Cairo Time (Ruba Nadda, 2009).

Carol
Her
Midnight in Paris
Crazy Heart
Up in the Air
(500) Days of Summer
Brokeback Mountain
Sideways
Eternal Sunshine of the Spotless Mind
Life is Beautiful
Il Postino: The Postman
Ghost
Cinema Paradiso

I have two movies to add:
In the mood for love (2000)- A lot of similarities between the two movies
Ikuru (1952) - lonliness is a key theme in both and falling in love with someone younger- both are heartbreaking.

The ones listed above, and in addition, Sofia Coppola's "Somewhere". Chris Evans' debut feature also takes from LiT quite a bit, it's called Before We Go.

I am not looking for character's isolation bs i am looking for cinematography, nice locations, the director that was casted due to nepotism is actually a good one i'm surpised sofia cortella what's her name? crapola francis what/
GILF cougar into incest horny af all the time give you love longtime all night long sucky sucky anal bukkakke gangbang orgy

Lost in Translation is my all time favorite movie, and I don't see this ever changing. While the below movies don't resonate emotionally with me like Lost in Translation does, I feel that they all are quiet movies that deal with loneliness and have that same surreal, dreamy tone and beautiful visuals.
Paris, Texas
Fallen Angels (1995) < end scene in this is on par with the final hug scene in Lost in Translation
Chungking Express
Days of Heaven
3-Iron (2004)
All the Real Girls
and more recently, Spike Jonze's "Her".