Philipp and Stount established the almost sure principle for lacunary trigonometric series with unweighted summands and stated that the approximate order might be close to 1/3. The proof of the sharpness of the approximate order close to 1/3 was given recently by Zhigang. The author of the present paper improves the result of Zhigang and obtains the best possible order as 1/4. Further the author discusses the general case of lacunary trigonometric series with weights and obtains the logarithmic order in some particular cases.