Does a unique non-clustered index help with locks?
Theoretically yes, practically no.

If SQL Server can guarantee that a field is unique, then it can build execution plans differently. Rob Farley blogged an example with AdventureWorks where the unique index isn't even shown in the execution plan, and yet its existence let SQL Server build a better plan.

If your data really does qualify for a unique index, then specifying it as unique will ensure that SQL Server always estimates 1 row to come back when you search for one value. That'll mean you're more likely to get more granular locks instead of table locks.

However, if you're worried about lock escalation, it's probably because you're not searching for equality. You're joining to other tables, or using range searches. In those cases, the uniqueness of an index isn't going to save you.