How did members of the Lucchese Crime Family move up in ranks?

I love your question! I don't know if you want a past history or
a more present description, but...

The Lucchese Family--one of the
original Five Families of New York-- was led by the "Three Tommys" for nearly 40 years. It was
first organized by Tommy Reina, who was murdered in 1930. ("Fat Joe"
Pinzolo led the family for a few months before his murder in 1930.) It was then led by
Tommy Gagliano until his death in 1951 (or possibly 1953).
Tommy Lucchese took over after Gagliano and turned the family into
one of the most powerful in NYC. He died of natural causes in 1967 and was followed by
Carmine Tramunti until he was imprisoned in 1974. He was later
assassinated behind bars. Anthony
"Ducks" Corallo served as boss until
1986 when he was arrested and turned over control to Vic Amuso.
Amuso's underboss was the bloody Anthony "Gaspipe" Casso, who later turned state's evidence in
1991. Corallo died in prison in 2000.

Amuso, too, was imprisoned in
1991 but continues as boss today while behind bars. His capos rule on the outside, led first by
Little Al D'Arco and then Little Joe DeFede; after DeFede was sentenced to prison in 1998, Steven
"Wonderboy" Crea took over. Crea was sentenced to prison in 2001, and consigliere "Lou Bagels"
Daidone took over. However, DeFede later turned state's evidence against Daidone, who was
imprisoned in 2003. Amuso, still in prison and still in control, created a triumvirat of three
capos to lead the family from that point on: Aniello "Neil" Migliore, Joseph "Joey Dee" DiNapoli
and Matthew Madonna remain Amuso's leaders today, although Madonna and DiNapoli have been
indicted several times. Crea was released from prison in 2006, but apparently is not involved in
top-level decision making.

So, to answer your question, murder and
imprisonment caused the rise of most of the family's bosses. Only the reclusive Gagliano and the
powerful Lucchese died of natural causes. The Lucchese Family is the smallest (but not the least
powerful) of the major families today, with only about 100 "made" members and as many as nine
captains.