Can someone tell me what "LSi" stands for, in regards to a Honda Civic 1.5 LSi?

I believe the LS is for the trim standard, the I is for Injection

luxury sports injection nice car i had on coupe vesion

In days of yore, cars had badging like 'Luxe', 'Grande Luxe' & 'Super Luxe' to designate different levels of trim. Nowadays, with the exception of a few makers, they use various combinations of letters and / or numbers and sometimes names without any particular meaning to show different levels of trim. This is done in a deliberately vague way as cars didn't used to sell very well if they were basic models or had little optional equipment. For your Civic, the base model was given various designations - DX, Bali, Marlin, etc., your LSi came next, there was a VEi, then the ESi was the best equipped model. The sporting variants were badged VTi. The i does usually signify fuel injection, but as there's virtually not a vehicle on the planet made today without injection, that little 'i' is still used. The VEi used Variable valve timing for Economy, which makes the VEi badge make sense, but the sporting VTi label was used rather than VSi, Sport or similar. The S in the LSi is deliberately vague - Standard? not really - Sport? nope - it's just a configuration of letters that looks the part!