Because Hymenocallis littarolis is a lily, an in vitro system using bulb scales should provide a convenient tissue for mutation breeding. There are a number of approaches that might work depending on your specific objectives.
Somaclonal variation – In vitro culture to regenerate shoots from the bulb scales.
Radiation – Irradiation of the bulb scales followed by in vitro culture to produce shoots.
Chemical mutagen – Mutagen treatment of bulb scales followed by in vitro culture to produce shoots. The type of mutagen can be matched to your objectives. For example, ethyl methanesulfonate (EMS) would result in nuclear point mutations (probably what you want); whereas, nitrosomethylurea (NMU) will result in a greater number of plastid mutations.
The first step would be to get the tissue culture system working, then inducing the mutations should be quite straightforward.
First you need to decide which mutagenic agent (physical or chemical) to use, Then you have need to make some experiments to determine the dose of application