Lipids contains hydrophobic and hydrophilic moieties, and it is generally insoluble in water. So my question is, whether is it possible to liquify or dissolve the lipids in water by attaining its phase transition temperature?
Everything is soluble in water, the question is how much, and this is detrmined by thermodynamics. Usually higher themporatyre results in higher solubility. I do not have at hand the of a typical oil, but I imagine it will be of the order of 30-50 ppm at room temperature, depending on polarity.
Depends greatly upon which lipid! Shorter chains are of course more soluble and just might become miscible at higher temps. Longer chains will simply separate into a second liquid layer. If you're using surfactant lipids, you could form vesicles especially at higher temps with a little agitation. Phospholipids have been studied extensively and I'm pretty sure you'll easily find the citations to others as well.
To liquefy means to change a substance from a solid to a liquid phase. Of course you can. By heating water, you heat the lipids and make a phase transition called melting.
Everything can be dissolved and it can be partially dissolved. Almost all lipids are partially soluble in water. A mixture of molecules always has greater entropy than the sum of the entropies of the pure components.