There are many ways to combine and hand knead pizza ingredients, and just about any dough recipe (other perhaps than a cracker crust dough recipe) can be converted to a hand-kneaded version, but this post might help in relation to your Lehmann dough: http://www.pizzamaking.com/forum/index.php/topic,576.msg5674.html#msg5674
(Reply 68). Since I wrote that post, I have discovered that it is possible to hand knead a larger amount of a high-gluten dough for a pizza size greater than 12". To do that, I advise using a high hydration (a high level of water of around 63%, by weight of flour) and also use one or more rest periods (autolyse or quasi-autolyse rest periods) during the kneading. During the rest periods, the dough will soften and be easier to handle. As noted in the above post, I made reference to the advice given by the King Arthur company to only use machines to do the kneading when using the King Arthur Sir Lancelot flour. It took me a long time to figure it out, but I ultimately concluded that the King Arthur advice was more relevant to making bread dough, which requires significant gluten development, than pizza dough, which should be slightly underkneaded (with less gluten development). If you are using a flour other than high-gluten flour, it should be even easier to hand knead and you may not need to use rest periods, although many members prefer to do so even in such cases. If you use a flour other than high-gluten flour, I also advise that you lower the hydration percent. The actual amount will depend on the type of flour used.
As for the type of oil to use, you can use just about any oil that you prefer. If you don't like olive oil, a good substitute among the types most commonly found in the supermarket would be canola oil. Professionals commonly use plain vegetable oil. Unless you like the flavor of corn oil, I would tend to avoid it. I think you will find that just about any oil can be used with the Lehmann dough formulation without really tasting it in the finished crust because the amount of oil in the basic Lehmann dough formulation is just 1%, which is too small to produce strong oil flavors in the finished crust.