The most common way to put together a piece of music like this is to simply take samples / recordings of musicians playing appropriate beats and phrases, and loop and trigger portions of those samples to make a new beat with a new feel. These days there are probably many types of products that you could use to do this, and thousands of individual products that have these capabilities. Looking back into hip-hop history, one noteable series of machine that was often used to make this kind of beat was the Akai MPC series, starting with the MPC60 in 1988. The audio technology used was much better than what was possible using most home computers at the time, but was still basic by today's standards (12-bit sampling at 40KHz) - that, in combination with the scratchy audio quality obtained by sampling from old vinyl records, is the kind of thing gives lo-fi beats their characteristic sound. Another aspect of the 'lo-fi' feel comes from drum beats with one rhythmic feel being forced into a slightly different feel.
MPC machines are still available today, as are many similar devices. but so is the possibility of doing this kind of sample manipulation in a DAW (digital audio workstation), or even using an audio programming language.
Likewise with the delay effect there is no one particular piece of equipment you need. Tape delay effects are often associated with lo-fi style production, and of course there are now many virtual tape delays available.
Of course it would also be possible to synthesize a piece like this without using samples of musicians playing - but starting by following something like the original process of sampling sections of music and retriggering them will help you understand where much of the characteristic sound comes from.