To be fair about it, at that time comic books, and their characters, were deemed somewhat simplistic and juvenile. (It should be noted, however, that they didn't necessarily start that way. Just as the early version of Superman was the personification of the New Deal, fighting corruption, graft and economic injustice, the initial Batman was created as a vigilante figure, as Bruce Wayne sought vengeance on all criminals after he saw his parents brutally murdered during a robbery attempt.) The environment that led to Jack Nicholson's portrayal of the Joker in 1989, or Ledger's this year, wasn't around for Romero in 1966.
Romero made one film with Lombard, playing a supporting role in "Love Before Breakfast" in 1936:
Carole and Cesar were on good terms, and she occasionally socialized with him off-screen (Romero was gay, but quite discreet). He spoke fondly of Lombard at a Los Angeles event honoring her in 1987.
Of Cuban descent, although he grew up in New York, Romero once said of his career: "I was never stereotyped as just a Latin lover in any case because I played so many parts in so many pictures. I was more of a character actor than a straight leading man. I did many kinds of characters -- Hindus, Indians, Italians. There were very few pictures where I ended up with the girl."
Prior to "Love Before Breakfast," Romero worked with the likes of Marlene Dietrich in "The Devil Is A Woman" and with William Powell and Myrna Loy in "The Thin Man" (his second film). From 1939 to 1941, he played the Cisco Kid in six low-budget westerns. His best movie work is generally considered to be in the 1947 costume drama "Captain From Castile."
Romero acted through 1990, then more or less retired. He died on New Year's Day 1994 at age 86.
Here's another picture of Romero and Lombard, alongside Robert Taylor and Irene Hervey, probably from about 1936 or so:
As I write this, the photo is currently available for auction at eBay (http://cgi.ebay.com/ROBERT-TAYLOR-CAROLE-LOMBARD-CESAR-ROMERO-8x10-PHOTO_W0QQitemZ150270372151QQihZ005QQcategoryZ18824QQssPageNameZWDVWQQrdZ1QQcmdZViewItem), but the auction will expire just before 7 p.m. Eastern. Moreover, it's a "buy it now" sale, for $24.99. And that's no joke.