Computer generated holography simulates the recording process of traditional optical holography by using computers to encode the amplitude and phase information of an object, and is able to achieve the information reconstruction of a virtual three-dimensional object in space, which has been widely used in the fields of three-dimensional display, optical storage and optical encryption. With the increasing complexity of 3D information, the amount of information storage requirements, and the amount of encrypted data, multiplexing in computer generated holography using space, time, wavelength and polarization dimensions has become an inevitable trend. However, with the explosive growth of information, the existing dimensions are about to be exploited. OAM holographic multiplexing technology has gained the attention of researchers. Traditional multiplexing modes use OAM as the only information carrier, which is prone to crosstalk and low information multiplexing rate. In order to solve the above problems, researchers have improved the orbital angular momentum holographic encryption scheme by combining the OAM with other optical dimensions, and the corresponding research results have been numerous.Thanks to the rapid development of vortex light field modulation technology, more and more intrinsic degrees of freedom of the beam have been exploited, such as notched beams, chiral light fields, and residual optical vortices. Researchers have applied these degrees of freedom to orbital angular momentum holography and achieved remarkable results, greatly enhancing the holographic information capacity and security performance. It is found that the generalized perfect optical vortices modulated by a free-lens phase have holographic preservation and mode selection properties similar to those of the spiral phase, and it is known that this novel and unique modulated phase has not yet been applied to orbital angular momentum holography.In this paper, we propose a multidimensional holographic encryption scheme that combines optical orbital angular momentum and multiparameter tunable free-lens phase. Multiple parameters in the generalized perfect optical vortex generated based on the free lens phase modulation are used as additional channels for multiplexed holography, and their potential as new coding degrees of freedom in holographic multiplexing is demonstrated. The influence of each parameter on the beam is analyzed by simulation. It is proved that the parameters are independent of each other, and that the focal length$f$, the radial displacement parameter $r_{\mathrm{0}}$, and the shape control factor$q$in the free lens phase have a modulation effect on the generalized perfect optical vortex, respectively. By applying each parameter of the free lens phase independently to holographic encryption, it is demonstrated that the parameter $f$ in the free lens phase is mode-selective in the axial direction and the radial displacement parameter $r_{\mathrm{0}}$ is mode-selective in the radial direction. In addition, inspired by the ellipticity-encrypted orbital angular momentum scheme, the potential of the shape control factor $q$in the free lens phase as an additional channel is exploited. Under the premise of reasonable design, the shape control factor has mode selectivity in the range of 1~20, so the shape control factor is added to the orbital angular momentum multiplexing holography scheme, which further increases the number of information channels and improves the security of the information. Simulation results show that the encrypted target image can be correctly reconstructed only when it is illuminated with a perfect optical vortex modulated by a free lens phase with an inverse topological charge $l$, the same radial displacement parameter $r_{\mathrm{0}}$ and the same focal $f$. On the basis of multi parameters coding to achieve high-capacity orbital angular momentum holography, it is experimentally verified that the resolution of the topological charge can be enhanced to 0.1 with the help of free lens phase to achieve fractional-order orbital angular momentum holographic multiplexing, which further expands the information capacity and improves the information utilization rate. This technique combines the orbital angular momentum holographic multiplexing technique with the optical field modulation technique, which improves the security of holographic encryption and increases the degree of freedom of the holographic channels, which can significantly improve the encryption and storage capacity of the information, and has a potential application in the field of communication.