I want mice model with apolipoprotein E deficiency (apoE-/-) and mice with LDL receptor deficiency (LDLR-/-). Can I get offspring possessing both characteristics by crossbreeding them? or i need to do double knockout.
I am not sure about your particular case, but in many many cases haplo deficient mice do not have the full KO phenotype. You can test the combinations (het/het, het/homo, homo/het) on your way to making the double knockouts. you'll likely want to start that process asap either way as it's the most efficient way to also generate the above mice.
Assuming that the double KOs are generally OK and not worse off than single ko in terms of survival/breeding (no idea about this personally for this particular case), and that you can genotype each of the 4 relevant alleles (ko and wt for each line).
You really can do it in principle with just one copy of each ko allele, but in practice you'll want to start with homozygote mice for each KO allele. You'll cross mate them together to make an F1 generation that are automatically double hets. You then mate multiple pairs of F1 mice together (you'll see soon why you want multiple pairs), and genotype to select for the appropriate breeders among the F2 animals (for each gene you KO, you have a 25% chance of F2 offspring being homozygote wt, 25% homozygote KO, 50% heterozygote; thus, you have 1/4 x 1/4 chance to get double KOs, or 6.25%)
Again assuming that the actual 2xKO genotype doesn't affect survival or breeding, you can then just breed the homozygous double knockouts and maintain the combined line like that.
Assuming, ApE-/- is fertile and LDLR-/- is fertile. When you cross them, you will get need to compund heterozygotes first, apoE+/-LDLR+/-, than you cross among themselves and you have chance (but small chance) of getting double knockout. It may take a year to get some double KOs,