Yes, from app lenders that score you on mobile-money activity instead. Banks and payroll lenders will still ask for a payslip.
Typically K100–K500. Lenders like Peony, Zigi and Kula Plus raise limits for repeat borrowers with a clean repayment record.
The serious ones do, and defaulting can shut you out of future credit. A small loan default can block a big bank loan later.
Avoid anything demanding an upfront fee, anything not on the Play Store, and lenders with no physical address or company name. Check Bank of Zambia licensing where it matters to you.