D&D 5E Warlock/Fighter Multiclass advice

[UngeheuerLich]

You have no chance to keep up if there is only a single fight per day without short rests. Your character profits mainly from short rests while the paladin mostly refreshes at long ones. The barbarian also. If your DM does not plan with short rests at all, and everyone can throw out daily resources at will I am sorry for you.
On the other hand, i am not sure if eldritch blast is your right answer to everything. With hex and hexblade curse and maybe eldritch knight you should be doing a lot more damage.

It is 2 beams at 1d10+1d6+8 damage and one extra attack at 1d8+1d6+8 damage. That averages to 47 damage without any problem. Use action surge and you should be ok.

 

[Ganders]

Is it worth it to get only 17 levels in warlock? Yes. The real question is when to take the fighter levels. Most people would say to get your 3rd level spells first (ftr1/warlock5), but after that it's a matter of priority. Some get the fighter level(s) next, some put it off for another 10 levels.

 

[ClockworkNinja]

not sure, though now i am wondering about an arcane archer/hexblade as a concept

Its not bad. 3 levels of warlock, choosing Bladepact Hexblade with Improved pact weapon is one way to get a magic longbow if your DM is stingy with such things. Along with all the other warlock goodies like spell slots that come back on a short rest and an invocation of your choice.

Personally not a fan of Arcane archer, would prefer EK or battlemaster with this, but you do you.