We present fluorescence and a random lasing enhancement effect due to the interaction between gold nanoparticles (AuNPs) and Rhodamine 6G (Rh6G) dye. Non-covalently bounded dyes in the proximity of nanoparticles are studied in three systems of varying dimensionality: from (i) three-dimensional freely distributed suspensions, through (ii) quasi-two-dimensional multilamellar liposomes, to (iii) solid two-dimensional thin layers. Liposomes facilitate the formation of stable AuNPs/Rh6G composition showing enhanced fluorescence, while solid thin films exhibit plasmon-assisted random lasing.