In Jain Dharma, lay people are generally allowed to read sacred texts in both major sects:

• Śvetāmbara
• Digambara

Within both traditions, śrāvakas and śrāvikās may study devotional texts, ethics texts, stories, prayers, and many scriptural works. However, access, language, and emphasis may differ by sect and sub-tradition.

A simple summary:

• Śvetāmbara traditions: lay study of Agamas and other sacred literature is widely accepted.
• Digambara traditions: lay study of approved sacred and philosophical texts is also accepted, though the canonical scriptural structure differs from Śvetāmbara.

So the short answer is: both main Jain sects allow laypeople to read sacred texts, with some differences in which texts are emphasized or considered authoritative.