You are right. As these analyses are routinely carried out in hospitals, autoanalysers can do them very conveniently. However, these equipments are not always available in universities and other research institutions.
Commercial kits are quite easy to find and there are a number of suppliers, but this usually involves doing an assay for each lipid class (TG, cholesterol, PL...).
Another possibility, if you have a HPLC by the hand, is HPLC coupled to an ELSD detector. You first isolate the lipoprotein fractions you want to analyse, you extract the lipids by a simple method (chloroform/methanol) and you can analyse the lipid extract by HPLC. In a single run you can get the major lipid classes (cholesterol esters, TG, cholesterol, diglycerides, monoglycerides and phospholipids).
You have the method in this paper https://www.researchgate.net/publication/8328473_Quantification_of_major_lipid_classes_in_human_triacylglycerol-rich_lipoproteins_by_high-performance_liquid_chromatography_with_evaporative_light-scattering_detection
I hope this was helpful
Article Quantification of major lipid classes in human triacylglycer...
TG and CT may be determined with commercial kits (Sigma, Wako, Roche...).
For HDL determination I suggest to precipitate apoB-containing lipoproteins with phosphotungstate reagent or Cl Mn1M: heparin (there are commercial kits) and determine cholesterol in the supernatant. For VLDL- and LDL- cholesterol/triglicerides you need to use more laborious methods such as FPLC or ultracentrifugation (these methods aldo isolate HDL).
TG and Chol can be determined with an enzymatic method (assays sold by several companies, s. Joan´s answer) which is running on an autoanalyser as well as in a microtiter plate (we have used it for mouse samples due to the limited volume of serum available). It´s an endpoint reaction and you can read it in an ELISA reader. To differentiate the lipoprotein subfractions you can use HPLC or lipoprotein electrophoresis but for the latter you need special technical equipment to read the gels afterwards. There are homogenous assays for autoanalyser who determine HDL-C and LDL-C but I have no experience whether you can run these assays outside of the machines. The best would be perhaps the precipiation method described be Joan for HDL-C. I am not familiar with procine lipoproteins, perhaps you can use the Friedewald equitation (LDL-C= TC - HDL-C + VLDL-C (TG/5 for mg/dl or TG/2.2 for mmol/l) to obtain the missing values.
Contact a clinical laboratory that analyzes human samples. Any local hospital can do this or a larger reference lab (i.e. QUEST diagnostics). I worked in a clinical lab for years and we often analyzed animal samples. They can also direct you on how to submit the samples. It may cost quite a bit but will save you having to troubleshoot your own methods.
I agree with others that the most straightforward and accessible approach is to measure cholesterol in whole plasma with commercially available enzymatic kits in conjunction with a precipitation method (also commercially available as a kit) to remove apoB containing lipoproteins (LDL and VLDL). This would provide you with total plasma cholesterol, HDL-cholesterol and non-HDL cholesterol (by difference). If you add a triglyceride assay of whole plasma, you may be able to additionally derive a calculated value for LDL-cholesterol as suggested by M. Hoffmann. However there are two caveats. First, you must use fasted plasma samples. Second, the estimate for VLDL-cholesterol from triglyceride values (VLDL-C=TG/5) is based on the composition of human VLDL. It may or may not be appropriate for porcine VLDL (it is not appropriate for rodent VLDL).
Other approaches, which are far more laborious and require specialized equipment include size exclusion chromatography (FPLC), sequential ultracentrifugation, and gradient ultracentrifugation - all followed by manual or online determination of the lipids.
What about FPLC of porcine serum/plasma? It gives you the lipoprotein profile and from analysis of the fractions you can estimate the composition of lipoproteins.
You must make yourself a bit familiar with analytical instruments and methods. A lot of analytical kits are commercially available for these parameters. Auto analyzers are very convenient, but if you do not have the facility, you may relay on UV-Vis semi auto with microcuvate. Many dry chemistry analyzers also handle these parameters.