They both held high positions side by side but it seems like Lucky got along with Carlo's superior more, meaning Anastasia.

Carlo was so sly that we may never know the truth.

Also, does anyone know who delivered the beating to Lucky on Coney Island when he was a low level associate? Did Lucky ever try and exact revenuonce he got to the top?

I read there was a meeting of Costello, Luciano, and Gambino in a hotel in Palermo.

In his book Luciano is quoted in 1961 saying about Gambino...

"Someday Gambino will be head of the whole outfit in the United States."

This is another quote from the book

“Meyer said it wouldn’t surprise him if one of these days, Albert took care of the Manganos and took over that outfit. [In 1951, a year later, Philip Mangano was murdered and Vincent disappeared; Anastasia became the new boss.] When that happened, Carlo was liable to get very ambitious. So Lansky asked me to send a message back to Vito and Carlo to tell ’em I knew what they was doin’ and to cut it out immediately, that I wouldn’t sit still for Vito tryin’ to muscle in on Anastasia. I also sent back a little private side message to Gambino. I told him I thought he was one of the best leaders in New York and maybe in ten or fifteen years, he could be head of it all. But he oughta keep his pecker down and be patient. That helped put a clamp on Vito for a few more years.”

Although they were on opposite ends on that issue, Lucky had respect for Carlo. I heard this recently in a documentary and I believe it to be true, that Lucky's best talent was recognizing talent in other people and using that not only to benefit himself but to everyone involved.

I would assume that it would be fairly positive and that Lucky would have seen Anastasia's "hit" as the part of doing business...

Well, one was a principal heroin exporter (Lucky), and the other was probably a principal heroin importer.

If we believe anecdotes in the Last Testament screenplay, that Carlo visited Lucky in Italy, then those meetings probably concerned the heroin trade.