I'm not sure what kind of lawyers you're talking about, but my answer is, definitely, yes. If they take the same LSAT and bar exam and equally qualified then I can't think of any reason why they shouldn't be "allowed" to be US lawyers. First of all, your question is not very intellectual and very ambiguous. How do you define "recent" immigrants? 2 years? 3 years? no matter what kind of standard you set, wouldn't it be arbitrary? If they speak English(obviously they do cause they don't offer LSAT in any other language than in English), and are equally qualified to pass the bar exam, then what does this country have to lose to "allow" them to become American lawyers? They would become part of the pool of law service, and if they're not competent enough then they will be automatically kicked out by the market mechanism. Say, they want to become an attorney general, which is a political appointee, then they would have to survive all the political screening.
I'm a foreign student on F-1 visa here, and I want to become an American lawyer. But eventually what I hope to do is go back to my country and become a M&A specialist. When American companies take over Asian companies or vice versa, who's gonna represent American companies? US lawyers. Law is the foundation of all cultures. If you have one more foreign US lawyer, you have one more strong comrade on the American side. When foreign students go back to their country after getting education here, they usually become enthusiastic lovers of this country, that's the soft power of America. Why do we want to deny that power and raise the barrier on them?