3 things increase your LUX earnings:
1) Assist cards. Higher LUX% means you will earn more.
2) Attack Power. Dealing more damage to the bosses will gain you more LUX.
3) Party Chain. After attacking the boss, if another party member attacks within 5 minutes there will be a chain. Chain provides bonus damage to the boss, earning you more LUX. To truly gain a significant chain damage, you need at least a chain of 20. So for weak parties, it is recommended to use 1BP hits till 20 chains are reached, then attack normally for the exponential damage. This strategy is still commonly used in active parties.
Edit: And of course, you earn double LUX during LUX Up Time.