"The beef ramen here is the tastiest."
I don't think any English speaker would use the word "ramen" for "lamian", whether or not they knew the words are related. Since they don't look or taste the same and "ramen" in English is already associated with either the Japanese dish or with instant noodles.
An English speaker who knew the Chinese name would say "lamian" and one who didn't would probably say something like "beef noodles" or "beef noodle soup".
In Japan and in English maybe. Not so much in China. In China 拉面 is almost always pulled noodles, a very different dish to ramen but they use the same characters. In Chinese if you were talking about the Japanese dish you'd likely say something like 日本拉面 and if you were talking about the Chinese dish you'd say 拉面 in Chinese but you wouldn't translate that to "ramen" in English because English "ramen" only has two meanings: the Japanese dish or instant noodles.
If you were speaking Chinese in a Japanese restaurant that might be enough context, but the Chinese sentence doesn't require such a special context since pulled noodle restaurants are everywhere in China and Japanese restaurants are a bit less common.