The Oilers are looking to move Gagner, among others, as they attempt to shake up their roster for the 2014-15 season.
The Kings have been in serious trade talks with the Edmonton Oilers and New York Islanders, while continuing conversations with other clubs.
Lombardi and Oilers GM Craig MacTavish had been discussing a deal for Edmonton center Sam Gagner.
According to two separate sources close to the situation, as talks continued to heat up for Gagner, the Islanders intensified their discussions with the Kings, which primarily revolved around left wing Thomas Vanek and defenseman Andrew MacDonald.
The Kings have also expressed an interest in Islanders left wing Michael Grabner.
It's unclear if any moves will be made today, though Lombardi is very active.
The Oilers are not interested in retaining parts of Gagner's salary, which the Kings requested. The Islanders may have to do the same with Vanek, depending on where he ends up.
The Kings are up against the salary cap and will need to be very creative in any trade they try to complete between now and March 5.
Lombardi wants to add a scoring left winger to his lineup and a top-four defenseman, and is hoping to address his depth up front.