General allometric scaling depends on specific calibrations. Pronciplles are depicted in B. Enquist lietrature and refs, https://msu.edu/~swensonn/EnquistEtAl_2007_nature.pdf , but as far cores you should specify about your target, if soil or or plant tissues.
In a simple agronomic term LAI can define as a quantifying that plant canopies in relation to effective ground area.. It is defined as the one-sided green leaf area per unit ground surfacearea (LAI = leaf area / ground area, m2 / m2) in broadleaf canopies.
You may have to use some equipment (eg. Licor 3000 leaf area meter or Licor LAI2200 plant canopy analyser.) if you want to do non destructive measurements. Licor 3000 has a photo-electric planimeter and easy to measure very small leaf area. If you want to do destructive sampling with small plants, you may have to plant number of plants at the same time and maintain them in a uniform growth conditions and with recommended spacing (to determine the ground area) in a field condition. Take reasonable number of plant may be 5-10 from a designated ground area and measure the leaf area. But I think your are planning for tree crops where you give larger space to grow for 7 years.
When you have a single plant on the ground, you have to determine the land area correctly. I would suggest you to mark the shaded area on the ground in the noon and treat this area as the ground area for LAI calculation.