Here are some Jain-inspired names starting with L:

• Lalit — graceful, attractive
• Lakshya — aim, goal
• Labdh — attained, achieved
• Labdhi — attainment, spiritual accomplishment
• Lalita — graceful, charming
• Lakshmi — prosperity, auspiciousness
• Lokesh — lord of the world
• Lokendra — supreme among beings
• Lalitesh — graceful lord
• Laxman — one with good marks, virtuous

If you want, I can also give:

• boy names
• girl names
• modern Jain names
• names with meaning