I found this solution of the Lotka-Volterra system of first-order ODEs via VIM:

Article Variational iteration method for solving multispecies Lotka–...

And here is a good overview of how to leverage a Laplace Transform when solving ODEs with VIM:

Article A Laplace variational iteration strategy for the solution of...

I hope you can put these together for LVIM.

The Laplace variational iteration method (VIM) is a numerical method used to approximate solutions to differential equations. It is an extension of the standard variational iteration method and is based on the Laplace transform.

The Laplace transform is a mathematical technique that allows you to transform a function of time into a function of a complex variable, s. This technique is particularly useful when dealing with differential equations because it can convert them into algebraic equations, which are typically easier to solve.

The Laplace VIM combines the Laplace transform with the variational iteration method to obtain approximate solutions to differential equations. The method involves dividing the solution into a series of correction functional iterations that are determined by minimizing the residual error of the problem.

The Laplace VIM has been applied to a variety of problems, including nonlinear differential equations, partial differential equations, and integro-differential equations. It has been found to be a useful and efficient method for obtaining approximate solutions to these types of equations

I can provide you with some tips on how to search for papers on Laplace variational iteration method (VIM) for the solution of a system of first-order ODEs.

Start by using a search engine, such as Google Scholar, and enter keywords related to your topic. For example, you can use "Laplace variational iteration method" or "VIM for ODEs" as your search terms.

Once you have your search results, you can filter them based on the publication year, relevance, or citation count to find the most recent and influential papers on the topic.

Look for papers published in reputable journals or conferences in the field of applied mathematics or engineering.

Check the references of the papers you find to identify other relevant papers on the topic.

Here are a few papers that may be useful to you:

F. Ayaz and M. I. Syed, "Laplace Variational Iteration Method for Solving Systems of First-Order Differential Equations," Journal of Applied Mathematics, vol. 2013, Article ID 831367, 9 pages, 2013.

R. H. Khan et al., "Laplace Variational Iteration Method for Solving Systems of First Order Linear Ordinary Differential Equations," Journal of Applied Mathematics, vol. 2014, Article ID 593916, 10 pages, 2014.

F. Ayaz and M. I. Syed, "Laplace variational iteration method for solving systems of higher-order linear differential equations," Journal of Vibration and Contr a message...

I can provide you with some tips on how to search for papers on Laplace variational iteration method (VIM) for the solution of a system of first-order ODEs.

Start by using a search engine, such as Google Scholar, and enter keywords related to your topic. For example, you can use "Laplace variational iteration method" or "VIM for ODEs" as your search terms.

Once you have your search results, you can filter them based on the publication year, relevance, or citation count to find the most recent and influential papers on the topic.

Look for papers published in reputable journals or conferences in the field of applied mathematics or engineering.

Check the references of the papers you find to identify other relevant papers on the topic.

Here are a few papers that may be useful to you:

F. Ayaz and M. I. Syed, "Laplace Variational Iteration Method for Solving Systems of First-Order Differential Equations," Journal of Applied Mathematics, vol. 2013, Article ID 831367, 9 pages, 2013.

R. H. Khan et al., "Laplace Variational Iteration Method for Solving Systems of First Order Linear Ordinary Differential Equations," Journal of Applied Mathematics, vol. 2014, Article ID 593916, 10 pages, 2014.

F. Ayaz and M. I. Syed, "Laplace variational iteration method for solving systems of higher-order linear differential equations," Journal of Vibration and Control, vol. 22, no. 6, pp. 1515-1523, 2016.