Routing Protocol for Low-Power and Lossy Networks (RPL) is an energy-efficient routing solution for IPv6 over Low-Power Wireless Personal Area Networks (6LoWPAN), recommended for resource-constrained devices. While RPL offers significant benefits, its security vulnerabilities pose challenges, particularly due to unauthenticated control messages used to establish and maintain routing information. These messages are susceptible to manipulation, enabling malicious nodes to inject false routing data. A notable security concern is the Routing Table Falsification (RTF) attack, where attackers forge Destination Advertisement Object (DAO) messages to promote fake routes via a parent nodes routing table. Experimental results indicate that RTF attacks significantly reduce packet delivery ratio, increase end-to-end delay, and leverage power consumption. Currently, no effective countermeasures exist in the literature, reinforcing the need for a security solution to prevent network disruption and protect user applications. This paper introduces a Lightweight Security Solution against Routing Table Falsification Attack (LiSec-RTF), leveraging Physical Unclonable Functions (PUFs) to generate unique authentication codes, termed Licenses. LiSec-RTF mitigates RTF attack impact while considering the resource limitations of 6LoWPAN devices in both static and mobile scenarios. Our testbed experiments indicate that LiSec-RTF significantly improves network performance compared to standard RPL under RTF attacks, thereby ensuring reliable and efficient operation.